Method and system for determining optical properties of semiconductor wafers

ABSTRACT

A method and system are disclosed for determining at least one optical characteristic of a substrate, such as a semiconductor wafer. Once the optical characteristic is determined, at least one parameter in a processing chamber may be controlled for improving the process. For example, in one embodiment, the reflectivity of one surface of the substrate may first be determined at or near ambient temperature. From this information, the reflectance and/or emittance of the wafer during high temperature processing may be accurately estimated. The emittance can be used to correct temperature measurements using a pyrometer during wafer processing. In addition to making more accurate temperature measurements, the optical characteristics of the substrate can also be used to better optimize the heating cycle.

RELATED APPLICATIONS

The present application is based upon and claims priority to aprovisional application having U.S. Ser. No. 60/696,608 filed on Jul. 5,2005.

BACKGROUND OF THE INVENTION

The accurate measurement of surface temperatures of hot objects is ofconcern in many industrial and scientific processes. For instance,temperatures must be accurately measured and controlled during thefabrication of semiconductor devices. In particular, the temperature ofsemiconductor wafers must be accurately monitored during rapid thermalprocessing of the wafers, during rapid thermal oxidation of the wafers,or during other processes which modify or add thin chemical films orcoatings to the surface of the wafers. For these semiconductorfabrication processes, the temperature of the substrate should be knownwithin a few degrees over a range which may extend from less than400.degree. C. to over 1,100.degree. C.

In the past, the temperature of hot objects was determined either using(1) contact methods or (2) non-contact methods. For instance, duringcontact methods, the hot object is contacted with a sensor such as athermocouple that is in turn connected to a temperature meter, whichindicates the temperature of the object. Conventional non-contactmethods of determining temperature, on the other hand, include using alight sensor such as an optical pyrometer that senses the thermalradiation being emitted by the object at a particular wavelength oflight. Once the thermal radiation being emitted by the object is known,the temperature of the object can be estimated.

When processing semiconductor materials for use in the electronicsindustry, it is generally preferable to use non-contact methods whenmeasuring the temperature of the semiconductor wafers. For instance, oneadvantage of non-contact methods is that the wafer can be rotated duringthe heating process, which promotes uniform temperature distributionthroughout the wafer. Rotating the wafer also promotes more uniformcontact between the flow of processing gases and the wafer. Besidesbeing able to rotate the wafers, another advantage to using non-contactmethods is that, since no temperature gauges need be attached to thewafer, the wafers can be processed much more quickly saving precioustime during semiconductor fabrication.

For all of the high temperature wafer processes of current andforeseeable interest, one of the more important requirements is that thetrue temperature of the wafer be determined with high accuracy,repeatability and speed. The ability to accurately measure thetemperature of a wafer has a direct payoff in the quality and size ofthe manufactured semiconductor devices. For instance, the smallestfeature size required for a given semiconductor device limits thecomputing speed of the finished microchip. The feature size in turn islinked to the ability to measure and control the temperature of thedevice during processing. Thus, there is increasing pressure within thesemiconductor industry to develop more accurate temperature measurementand control systems.

In this regard, the chief disadvantage of conventional non-contactoptical pyrometry systems for determining temperature is that thesystems measure an apparent temperature rather than the true temperatureof the wafer. In particular, a real surface emits radiation lessefficiently than an ideal or perfect blackbody. Through theory andcalculation, once the emitted radiation of a blackbody is known, thetemperature of the blackbody can be calculated. A real body, however,such as a wafer, emits only a fraction of the radiation that would beemitted by a blackbody at the same temperature. This fraction is definedas the emittance of the real object. Thus, when sensing the radiationbeing emitted by a real body, a pyrometer generally indicates anapparent temperature that can be different from the true temperature ofthe object.

Thus, in order to measure the true temperature of a real body using apyrometer, the indicated temperature must be corrected to account forthe emittance. Unfortunately, the emittance of a real body is generallyunknown and is very difficult to measure accurately. Further, theemittance of semiconductor wafers varies from wafer to wafer. Theemittance is a property of the wafer and depends on several parameters,such as the chemical composition of the wafer, the thickness of thewafer, the surface roughness of the wafer, any coatings present on thewafer and the wavelength at which the pyrometer operates.

In addition to being able to determine the emittance of thesemiconductor wafer, problems in accurately determining the temperatureof the wafer can also occur when the wafer is semi-transparent at thewavelength at which the pyrometer operates. This problem is especiallyprevalent at lower temperatures.

In the past, some methods have been proposed for measuring theproperties of the semiconductor wafer prior to processing the wafer orduring processing of the wafer. For example, U.S. Pat. No. 6,056,434discloses a method by which the reflectivity of the semiconductor waferis measured to assist in determining the emittance of the wafer.

The present disclosure is directed to further improvements in methodsfor determining the optical properties of substrates, such assemiconductor wafers that are to be processed in thermal processingchambers. The properties or characteristics of the wafer that aredetermined according to the present disclosure may then be used tobetter control the heating process and/or the manner in which thesubstrate is heated.

SUMMARY OF THE INVENTION

The present disclosure is generally directed to a method for determiningthe optical characteristics of a substrate, such as a semiconductorwafer in order to more accurately heat the wafer during a heatingprocess or to otherwise better control various system components orvariables during the heating process. The system and method disclosedallow for improved accuracy and wafer temperature readings by aradiation sensing device, such as a pyrometer, or for improvedmeasurements and/or prediction of the thermal radiative properties ofthe substrate. In one embodiment, the optical characteristics of thesubstrate determined according to the method can be supplied to acontroller for improved wafer temperature control.

In one embodiment, for example, the present disclosure is directed to amethod for determining at least one optical characteristic of asemiconductor wafer. The method includes the steps of emitting lightonto a first surface of the semiconductor wafer having a particularthickness. The light that is emitted onto the first surface of thesemiconductor wafer is directed through an optical pathway that isconfigured to separate the light reflected from the first surface fromlight that passes through the wafer and is reflected off a second andopposite surface of the wafer.

Once the light reflected from the first surface is separated from thelight reflected from the second surface, the light reflected from thefirst surface can be detected using a detector. The detector may be, forinstance, any suitable photosensor and may be configured to detect theamount of light reflected from the first surface at a certain wavelengthor at a certain wavelength range.

In accordance with the present disclosure, based on the amount ofdetected light reflected from the first surface, at least one opticalcharacteristic of the semiconductor wafer is then determined. Thecharacteristic may comprise a reflectivity of the first surface, anemissivity of the first surface, an absorptivity of the first surface,or a transmissivity of the first surface. Alternatively or in addition,the optical characteristic may comprise a reflectance, an emittance, anabsorptance or a transmittance of the semiconductor wafer. Further,instead of or in addition to determining at least one opticalcharacteristic of a first surface of the semiconductor wafer, the methodcan also be used to determine at least one optical characteristic of anopposite surface of the wafer.

The optical pathway that is used in order to separate the lightreflected from the first surface from the light reflected from thesecond surface may vary depending upon the particular application. Theoptical pathway, for example, may comprise a plurality of opticaldevices. The optical devices can comprise mirrors, lenses, apertures,and the like. In one particular embodiment, for instance, the opticalpathway includes a first lens and a second lens which direct the lightonto a particular location of the first surface of the semiconductorwafer. After the light reflects off the first surface, the light thenagain passes through the second lens. From the second lens, the light isreflected off a mirror and passes through a third lens so as to befocused onto a light detector. It should be understood, however, thatthe above embodiment merely represents one example of an optical pathwaythat may be used in the present disclosure.

The manner in which the light reflected from the first surface isseparated from the light reflected from the second surface as the lighttravels through the optical pathway may also vary from application toapplication. Separating the different light beams, for example, may becarried out by adjusting the focal length of one or more lenses in thesystem. Alternatively or in addition, the system may include variousapertures or filters in order to separate the different light streams.In still other embodiments, the light may be emitted onto the firstsurface of the semiconductor wafer at a distribution of angles ofincidence in order to separate the light reflected from the firstsurface from the light reflected from the second surface.

The light source that may be used in order to emit light onto the firstsurface of the substrate can vary depending upon the particularapplication. For instance, in one embodiment, the light may comprise abroad band light source. Alternatively, the light source may emit alaser beam.

Once at least one optical characteristic of the semiconductor wafer isdetermined based upon the above method, the optical characteristic maybe used and incorporated into various systems and processes. Forexample, in one embodiment, the one or more optical characteristics thatare determined are used to control a heating process for thesemiconductor wafer. In this embodiment, based upon the opticalcharacteristic, at least one system component in a process for heatingthe semiconductor wafer can be controlled.

For instance, in one embodiment, the system component may comprise atemperature measurement system that includes a radiation measuringdevice, such as a pyrometer, that senses the amount of radiation beingemitted by the semiconductor wafer during heating for determining thetemperature of the semiconductor wafer. The amount of detected lightfrom the first surface may be used to determine the emittance of thesemiconductor wafer for use in determining the temperature of thesemiconductor wafer in conjunction with the amount of radiation beingsensed by the radiation measuring device.

In this embodiment, for example, the radiation sensing device sensesradiation being emitted by the semiconductor wafer at a certainwavelength. The amount of light that is reflected from the first surfaceof the semiconductor wafer is detected at the same wavelength at whichthe radiation sensing device operates. The measurement of the amount ofreflected light that is detected from the first surface of thesemiconductor substrate may also occur at a temperature less than about100° C. For example, the amount of detected light from the first surfaceof the semiconductor wafer may be used to determine reflectance andemittance of the semiconductor wafer at temperatures where thetransmittance of the semiconductor wafer is less than 0.1 at thewavelength at which the radiation sensing device operates. Moreparticularly, in one embodiment, the reflectance and/or the emittancethat is determined at a temperature less than about 100° C. can be usedto predict the emittance of the substrate at higher temperatures using,for instance, a model.

In an alternative embodiment, the system component may be related to theheating device that is used to heat the wafer. During the heatingprocess, for instance, a power controller for a heating device that isused to heat the semiconductor wafer may be adjusted. The heating devicemay comprise, for instance, an array of light energy sources, a heatedsusceptor, or a mixture of both. The amount of detected light from thefirst surface of the semiconductor wafer may be used to determineabsorptance of the semiconductor wafer during heating for adjusting thepower controller and thereby selectively increasing or decreasing theamount of energy being used to heat the semiconductor wafer. In thismanner, the absorptance is used to optimize the power or energy setting.In this embodiment, the light that is reflected from the first surfaceof the semiconductor wafer and detected may be at a wavelength rangethat substantially overlaps a range of wavelengths of electromagneticradiation that is used to heat the wafer.

In still another embodiment of the present disclosure, the opticalcharacteristics of the semiconductor wafer that are determined may beused to correct the readings of the radiation sensing device at lowertemperatures where transmittance is greater than 0.1 at the wavelengthat which the radiation sensing device operates. In this embodiment, alight source emits light that is incident on the first surface of thewafer and the amount of light reflected from the first surface isdetected separately from the amount of light that is reflected from theopposite surface of the wafer. For example, an optical pathway may beused in order to separate the reflected light from the first surface ofthe wafer from the reflected light from the opposite surface of thewafer. This information is then used to determine a reflectivity of bothsurfaces of the wafer. The reflectivities are then used to determinetransmittance and emittance of the semiconductor wafer at temperatureswhere the transmittance of the semiconductor wafer is greater than 0.1at the wavelength at which the radiation sensing device operates. Thetransmittance and emittance that are determined may then be used tocorrect for temperature measurements that are taken with the radiationsensing device.

In a similar manner, the method of the present disclosure can also beused to control the power or energy level of the heating device at lowertemperatures as well. In this embodiment, however, the reflected lightoff the first surface of the semiconductor wafer and off the secondsurface of the semiconductor wafer are detected at a wavelength rangethat substantially overlaps with the wavelength range of theelectromagnetic radiation that is used to heat the wafer. In thismanner, absorptance can be determined and used to optimize power orenergy settings.

The optical characteristics of the semiconductor wafer may be determinedas described above within the thermal processing chamber or outside ofthe chamber. For instance, in one embodiment, the opticalcharacteristics may be determined at any suitable location. Forinstance, the measurements may occur at a station on a robotic arm or ina separate chamber. Once the optical characteristics are determined, thewafer can then be transferred to a thermal processing chamber forundergoing various processes. The optical characteristics can then beused to control at least one system component in the thermal processingsystem.

Other features and aspects of the present invention are discussed ingreater detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of the present invention, including thebest mode thereof to one skilled in the art, is set forth moreparticularly in the remainder of the specification, including referenceto the accompanying figures, in which:

FIG. 1 is a side view of one embodiment of a thermal processing chamberthat may be used with the method and system of the present invention;

FIG. 2 is a plan view of one embodiment of a system made in accordancewith the present invention;

FIG. 3 is a side view illustrating a light beam being emitted onto asubstrate, such as a semiconductor wafer;

FIG. 4 is a side view illustrating two light beams being emitted onto asubstrate such as a semiconductor wafer;

FIG. 5 is a side view illustrating another embodiment of two light beamsbeing emitted onto a substrate such as a semiconductor wafer;

FIG. 6 is a side view of one embodiment of an optical pathway that maybe used in accordance with the present invention;

FIG. 7 is a side view of another embodiment of an optical pathway thatmay be used in accordance with the present invention;

FIG. 8 is a side view of another embodiment of an optical pathway thatmay be used in accordance with the present invention;

FIG. 9 is a graph illustrating light intensity based on position as willbe described in more detail below;

FIG. 10 is a side view of still another embodiment of an optical pathwaythat may be used in accordance with the present invention;

FIG. 11 is a side view of another embodiment of an optical pathway thatmay be used in accordance with the present invention;

FIG. 12 is a side view of yet another optical pathway that may be usedin accordance with the present invention;

FIG. 13 is a side view of another embodiment of an optical pathway thatmay be used in accordance with the present invention;

FIG. 14 is a side view of another embodiment of an optical pathway thatmay be used in accordance with the present invention;

FIG. 15 is a side view illustrating one embodiment for dual-sidedillumination of a wafer;

FIG. 16 is a side view illustrating another embodiment for dual-sidedillumination of a wafer;

FIG. 17 is a side view illustrating an embodiment for illuminating awafer at different locations in accordance with the present disclosure;

FIG. 18 is a side view illustrating a light beam being emitted onto asemiconductor wafer containing front side and back side coatings;

FIG. 19 is a side view illustrating the propagation of rays of lightincident on the front surface of a wafer and the values for intensity oflight at various positions;

FIG. 20 is a graphical illustration of the temperature dependence ofoptical properties of a wafer where the substrate has atemperature-dependent absorption coefficient; and

FIGS. 21 through 26 are different embodiments of flow charts of methodsfor measuring wafer properties in accordance with the presentdisclosure.

Repeat use of reference characters in the present specification anddrawings is intended to represent the same or analogous features orelements of the present invention.

DETAILED DESCRIPTION

It is to be understood by one of ordinary skill in the art that thepresent discussion is a description of exemplary embodiments only, andis not intended as limiting the broader aspects of the presentinvention.

In general, the present disclosure is directed to a method and to asystem for determining at least one optical characteristic of asubstrate and then using the characteristic to control a process that iscarried out on the substrate. For example, in one embodiment, thesubstrate may comprise a semiconductor wafer and the opticalcharacteristic is used to better determine and control the temperatureof the wafer during a heating process. Alternatively, the opticalcharacteristic may be used to control a heating device that is used toheat the wafer.

It should be understood, that the methods of the present disclosure maybe used in conjunction with other substrates in addition tosemiconductor wafers. For instance, the methods of the presentdisclosure may be used with any suitable substrate, such as ribbons,films, fibers, filaments, and the like.

When the substrate comprises a semiconductor material, the methods ofthe present invention can be used during heat treatment of thesubstrate, during oxidation of the substrate, or during other processeswhich modify or add films to the surface of the substrate. Otherprocesses that may be used in accordance with the present invention, forinstance, include any suitable film deposition process, such as achemical vapor deposition process or an atomic layer deposition process.The principles of the present invention may also be used during plasmaprocessing for depositing a material on a substrate or for etching asubstrate.

Referring to FIG. 1, one exemplary embodiment of a system generally 10that may be used in the process of the present invention for processingsubstrates, such as semiconductor wafers, is illustrated. System 10includes a processing chamber 12 adapted to receive substrates such as awafer 14 for conducting the various processes. The wafer 14 may beplaced in the processing chamber 12 on a substrate holder 15 that,optionally, may be configured to rotate the wafer. Chamber 12 isdesigned to heat the wafer 14 at very rapid rates and under carefullycontrolled conditions. Chamber 12 can be made from various materials,including certain metals, glasses and ceramics. For instance, chamber 12can be made from stainless steel or quartz.

When chamber 12 is made from a heat conductive material, the chamber mayinclude a cooling system. For instance, as shown in FIG. 1, chamber 12includes a cooling conduit 16 wrapped around the perimeter of thechamber. Conduit 16 is adapted to circulate a cooling fluid, such aswater, which is used to maintain the walls of the chamber 12 at aconstant temperature.

Chamber 12 can also include a gas inlet 18 and a gas outlet 20 forintroducing a gas into the chamber and/or for maintaining the chamberwithin a preset pressure range. For instance, a gas can be introducedinto chamber 12 through gas inlet 18 for reaction with the wafer 14.Once processed, the gas can then be evacuated from the chamber using gasoutlet 20.

Alternatively, an inert gas can be fed to the chamber 12 through the gasinlet 18 for preventing any unwanted or undesirable side reactions fromoccurring within the chamber. In a further embodiment, gas inlet 18 andgas outlet 20 can be used to pressurize the chamber 12. A vacuum canalso be created in the chamber 12 when desired.

During processing, the chamber 12 can be adapted to rotate the wafer 14using a wafer rotation mechanism 21. Rotating the wafer may promotegreater temperature uniformity over the surface of the wafer and maypromote enhanced contact between the wafer 14 and any gases introducedinto the chamber. It should be understood, that besides semiconductorwafers, the chamber is also adapted to process optical parts, films,fibers, ribbons and other substrates having any particular shape.

One or more heating devices may be placed in association with thechamber for heating the wafer 14 during processing. In this embodiment,a heating device 22 includes a plurality of lamps 24, such as tungstenhalogen lamps, arc lamps, lasers or mixtures thereof. The heating device22 can include a reflector or set of reflectors for directing thermalenergy being emitted by the heating device onto the wafer 14. As shownin FIG. 1, the lamps 24 may be placed above the wafer 14. It should beunderstood, however, that the lamps may be placed at any particularlocation. For instance, additional lamps may be included within thesystem 10 that are positioned not only above the wafer 14 but below thewafer 14 as well.

As an alternative to using a plurality of lamps or in addition to thelamps, the processing chamber may also include various other heatingdevices. For instance, the heating device may emit any suitableelectromagnetic radiation configured to heat the substrate. The heatingdevice may emit, for instance, radio frequency or microwave energy. Inother embodiments, the substrate may be heated in a hot wall environmentor through convective heating. A substrate may also be heated withenergy beams. The energy beams may comprise, for instance, plasma beams,electron beams, or ion beams.

In one particular embodiment, the processing chamber may include aheated susceptor. For instance, a heated susceptor may be positionedabove or below the wafer for heating the wafer without contacting thewafer. Such heated susceptors are well known in the art.

As shown in FIG. 1, the one or more heating devices, such as the lamps24 may be equipped with a gradual power controller 25 that can be usedto increase or decrease the thermal energy being emitted by the heatingdevice.

The thermal processing chamber 10 further includes a plurality ofoptical fibers or light pipes 28 which are, in turn, in communicationwith a plurality of corresponding light detectors 30. The optical fibers28 are configured to receive thermal energy being emitted by the wafer14 at a particular wavelength. The amount of sensed radiation is thencommunicated to the light detectors 30 which generate a usable voltagesignal for determining the temperature of the wafer. In one embodiment,each optical fiber 28 in combination with a light detector 30 comprisesa pyrometer.

During the process, system 10 may be designed such that the opticalfibers only detect thermal radiation being emitted by the wafer 14 andnot detect radiation being emitted by the lamps 24. In this regard,system 10 includes a filter 32 which inhibits thermal radiation beingemitted by the lamps at the wavelength at which the light detectors 30operate from entering the chamber 12. Filter 32 can be a window and, inone embodiment, can be comprised of fused silica or quartz.

As described above, the temperature of the semiconductor wafer 14 ismonitored during processing by the optical fibers 28 and the lightdetectors 30. Specifically, the light detectors 30 sense the amount ofradiation being emitted by the wafer 14 at a particular wavelength fordetermining the temperature. In order to accurately calculate thetemperature based upon the amount of radiation sensed by the lightdetectors 30, various characteristics of the wafer 14 must be known orotherwise estimated. For example, temperature determinations are basedupon the reflectance, transmittance, and/or the emittance of the wafer14 which are often times difficult to predict or estimate. These valuescan change not only based upon the temperature of the wafer 14 but alsocan change due to any structures that may be built on the wafer 14 as itis processed.

In the past, many attempts have been made in order to devise anon-contact temperature measurement system that is capable of eitherdetermining or estimating the characteristics of the wafer 14. In someembodiments, for instance, the measurements or determinations are madewhile the wafer is being processed. For example, U.S. Pat. No.6,056,434, which is incorporated herein by reference, discusses anin-situ temperature determination process that utilizes a reflectometer.

In other embodiments, attempts have been made to measure variouscharacteristics of the substrate before it is processed. As describedabove, however, the optical properties of the substrate may change withtemperature. Also, some of the materials present on the substrate mayundergo a transformation or other materials may be formed on thesubstrate that affect the structure and optical properties of thesubstrate. These obstacles have limited the ability to usepre-processing characterization as a means for improved processing.

One of the main problems arises because the optical absorption ofsemiconductor materials, such as silicon, is strongly affected by itstemperature and doping. For example, a lightly-doped silicon wafer istypically semitransparent at room temperature for wavelengths >˜1.1 μm.As a result, a typical measurement performed at room temperature atwavelengths greater than about 1.1 μm will be affected by theconsequences of light being transmitted through the substrate andreflected from the opposite surface of the wafer. When the wafer isheated in the processing system, the absorption coefficient of thesilicon rises very rapidly with temperature and the wafer becomes moreopaque. This change leads to large changes in the reflectance andemittance of the wafer. In this case, the room temperature measurementof properties is less useful for improving temperature measurement orcontrol.

The present disclosure is directed to a method and system fordetermining the optical properties of a substrate, such as asemiconductor wafer, prior to processing the wafer. In accordance withthe present invention, various optical properties of the wafer aremeasured or otherwise determined that can be used not only to assist inmaking more accurate temperature determinations, but can also be used tocontrol the heating device in a manner that optimizes absorption ofthermal energy. Of particular advantage, the information obtained usingthe methods of the present invention allow for temperaturedeterminations not only at lower temperatures but also at highertemperatures. The methods of the present invention may be carried outoutside of the processing chamber prior to processing the wafer.Alternatively, the determinations may also be carried out inside theprocessing chamber itself.

Prior to discussing the principles of the present invention, a briefdescription of how a light beam interacts with a substrate may beuseful. For example, FIG. 3 shows a representative wafer-like structurethat is illuminated by a ray of light, A0, that is incident on itssurface at an angle of incidence θ_(o). The wafer-like structure mayhave coatings and device features at its top (WF) and bottom (WB)surfaces, which may affect the reflectivity and transmissivity of thesesurfaces. Some of the power in the incident ray is reflected at the topsurface, forming a reflected ray of light, R1. A second portion of theray penetrates the front surface (WF), and forms an internal ray, A1.This ray propagates at a different angle, θ_(i), as a result ofrefraction caused by the difference between the refractive index of thewafer and the incident medium that contains ray A0. As the ray A1propagates through the thickness of the wafer its intensity may bereduced by absorption of energy within the wafer. Typically, thisabsorption depends on the path length through the wafer through anexponential relationship referred to as Beer's law.

When the ray A1 reaches the back surface of the wafer a portion of it istransmitted through the surface to form a ray T1. A second portion isreflected from the back surface WB and forms a second internal ray, A2.If the back surface WB of the wafer at the point where A1 reaches it isparallel to the front surface of the wafer where A0 was incident, thenthe ray T1 will propagate in a direction parallel to the original rayA0, provided that the refractive index of the medium beyond the back ofthe wafer is the same as the medium containing A0. The ray A2 will alsobe at the same angle to the wafer normal as for A1. The ray A2 will alsobe attenuated by absorption as it heads back towards the front surfaceWF of the wafer, where part of it will be transmitted to form a ray R2,and part of it will be reflected to form another internal ray A3.

Internal ray A3 then follows behavior identical to that for A1,returning to the back surface WB of the wafer and generating a secondtransmitted ray T2, and yet another internal ray A4. A4 then follows thebehavior identical to that for A2, returning to the wafer surface andgenerating an external ray R3, and an internal ray A5. Hence we see thata single ray A0, incident on the surface of the wafer can generate aninfinite series of reflected rays such as R1, R2, R3, etc. and aninfinite set of transmitted rays T1, T2, etc.

In practice, the finite reflectivity and transmissivity of the surfaces,combined with the finite absorption along the path of each of theinternal rays through the substrate thickness, usually lead to a fairlyrapid attenuation of the power of the rays as the number of internalreflections rises. However, reflectance measurements can be stronglyaffected by the degree of light transmission through the substrate, ifthe measurement apparatus collects energy from rays such as R2 and R3 inaddition to the first reflection, R1. Likewise a measurement oftransmittance will be affected by collection of the energy in themultiply-reflected rays such as T2, as well as the first ray T1.

FIG. 4 illustrates the effects of such multiply-reflected rays on areflectance measurement, in a scenario rather like FIG. 3, exceptshowing the incident beam of light as a collimated beam of light with afinite size, rather than the idealized single ray of FIG. 3.

Two extreme rays A and B are shown to represent the outer limits of thecollimated beam of light, H0. The beams of light reflected at the twowafer surfaces (e.g. HR1 and HR2) overlap as shown at OVR1, so that if alight detector were used in an attempt to measure reflectivity, thelight collected by the detector would include not only light reflectedoff the front surface of the wafer, but also light reflected from theback surface of the wafer. Such a measurement would not distinguishbetween light reflected from the front and from the back of the wafer.

Likewise, the measurement of the transmittance will also result in ameasurement that is affected by multiple reflections of light within thesubstrate, e.g. as a result of overlap OVT1 between beams HT1 and HT2.

The present disclosure is generally directed to a method and system foremitting light onto a substrate, such as a semiconductor wafer andseparating through various means the amount of light reflected from thefront surface of the wafer from the amount of light reflected from theback surface of the wafer. Once the light is separated, accuratemeasurements of the reflectivity of each surface can be conducted. Thepresent inventor has found that this information can be useful incontrolling at least one parameter in a processing chamber when thewafer is later processed as will be described in greater detail below.

For example, referring to FIG. 5, one embodiment of an approach foreliminating the effect of multiple reflections is illustrated. In thiscase, the size of the incident beam of light, H0, and theangle-of-incidence on the substrate have been selected to separate thebeams of light reflected from the different surfaces (HR1, HR2, HR3etc.). The locations where the incident beam of light is reflected fromthe front (HR1) of the substrate and the location where the lightreflected from the back surface of the substrate (HR2) reaches the frontsurface do not overlap. As a result, there are several beams ofreflected light, which are spatially separated. The light in these beamscan fall on different detectors, or on an array of sensors. Theintensity of the light reflected in the first reflection of the incidentbeam is only affected by the reflectivity of the front surface of thesubstrate, whereas that in the second reflected beam is affected by thereflectivity of both the front and the back of the substrate as well asthe absorption coefficient of the substrate.

In some cases only the reflectivity of the front surface may be ofinterest, but by collecting the light in separate beams it is possibleto analyze the optical properties of the wafer more completely. Forexample, by collecting two beams of reflected light, information can bededuced about both surfaces of the wafer, and/or about the absorptioncoefficient of the wafer. Similar benefits can apply to analysis of thedifferent components of transmitted light, HT1, HT2, etc., shown in FIG.5. Furthermore, by making separate measurements with light incident fromeither the front or back of the wafer, even more information can beobtained and/or the magnitude of errors in the estimates of opticalproperties of the wafer can be reduced.

When carrying out the method as shown in FIG. 5, the one or moredetectors used may comprise any suitable device capable of measuring theintensity of a light beam at a particular wavelength or at a range ofwavelengths.

Despite the advantages of using the configurations of FIG. 5, in someembodiments, it may be difficult to implement for all types ofsubstrates, especially for those that are relatively thin and where therefractive index is relatively large. In such circumstances, thedistance between the position where the incident beam of light impingeson the top surface and the position where the beam of light reflectedfrom the back of the substrate impinges on the top surface may be quitesmall, leading to the need for a very small incident beam of light.However, laser light sources may be used to provide higher intensityillumination for narrow beams of light.

In another embodiment, various techniques may be used in order todetermine and differentiate the amount of light reflected off the frontsurface of the wafer versus the amount of light reflected off the backsurface of the wafer, even in cases where the reflected beams partiallyoverlap. For example, as long as the overlap of light is only partial,the degree of overlap may be calculated from geometrical calculations.Further, the conditions of the overlap can be varied by changing thesize or shape of the incident beam or the angle of incidence, which willallow for a determination of the amount of light being reflected off thefront surface. For example, changing the angle of incidence of thecollimated beam of light HO may alter reflectivity and the path lengththrough the substrate. In one particular embodiment, for instance, inone condition the detected reflected light off the substrate may includeall the reflected components R1, R2, R3, etc. as shown in, for instance,FIG. 3. In a second condition by altering the angle of incidence, theremay be no overlap in the components of the reflected beams. Similartechniques may then be used for analysis of the transmitted light aswell.

In other embodiments, instead of or in addition to manipulating thelight source for separating the different light components, an opticalpathway may be devised that is configured to separate the differentlight components. Once the different light components are separated, anyof the light components can be detected or measured to the exclusion ofthe other light components. For example, in one embodiment, lightreflected from the top surface of a substrate may be separated fromlight being reflected from the bottom surface of the substrate. Theamount of light reflected from the top surface and/or the amount oflight reflected from the bottom surface may be detected for determiningvarious properties of the substrate. For instance, light reflected fromthe top surface and light reflected from the bottom surface of thesubstrate each provide information about various characteristics of thesubstrate.

For example, FIG. 6 illustrates an alternative approach fordiscriminating between light reflected from the top surface and thebottom surface of a wafer-like substrate. As shown, a ray of light froma light source, S, is propagated through an optical pathway thatincludes lenses and mirrors. Ray A1 is emitted by S and then collectedby the lens L1 that forms a collimated beam, represented by the ray A2.A2 passes through a mirror M and continues as ray A3. L2 is a lens thatfocuses the light, forming the ray A4 that impinges on the front surfaceof the wafer WF.

Part of the ray A4 is reflected from WF, forming the ray ARF1. ARF1 iscollected by the lens L2, which recollimates it to form the ray ARF2.The ray ARF2 is reflected from the mirror M forming the ray ARF3. ARF3is collected by the lens L3, which focuses it, forming the ray ARF4,which impinges on a detector D2.

A second part of the ray A4 is transmitted through the surface WF of thewafer, forming an internal ray AT1. Part of AT1 is transmitted throughthe back surface of the wafer, forming a transmitted ray AT2. A secondpart of AT1 is reflected from back surface WB, forming the internal rayATRB1. Part of ATRB1 is then reflected at the front surface forming theinternal ray ATRBRF1. ATRBFR1 then propagates to the back surface, andsome of it is transmitted through back surface of the wafer WB, forminga second transmitted ray ATRBRF2. A second portion of ATRBRF1 (notshown) will also be reflected at WB, to form the infinite series ofinternal rays, as was discussed above. Part of ray ATRB1 is transmittedthrough the front surface WF, to form a second reflected ray ATRB2.

If both ray ARF1 and ATRB2 are collected by the optics of the reflectedlight measurement system and arrive at the same detector element, thenthe reflectivity of the back surface of the wafer will influence thereflectance measurement.

ATRB2 is collected by lens L2 and focused to form the ray ATRB3, whichis reflected by the mirror M to form ATRB4, which is focused by lens L3to impinge on a detector D3 as ATRB5.

If D2 and D3 are separate detectors then it is possible to discriminatebetween the two reflected rays. In this case the measurement fromdetector D2 represents reflection from only the front surface of thewafer. The measurement from detector D3 may also be useful for analysisof the properties of the wafer, because its intensity is affected by theabsorption of light within the wafer, by the transmissivity of WF, andby the internal reflection from WB.

In some systems, the source S may emit light over a range of angles.Although it may be possible to restrict the range of angles of incidencethrough the use of apertures, this can result in loss of signal strengthfor the measurement since the intensity of light is reduced. Thebehavior of rays that propagate through the optical system may beanalyzed at different angles to the optical axis. FIG. 7 illustrates thebehavior of two rays emitted from S as they pass through the sameoptical system as considered in FIG. 6. In this case ray A and ray B areemitted at the same angle to the optical axis, but they are on oppositesides of the axis. Their behavior is symmetrical about the axis. RaysARF and BRF represent the two rays that are reflected from the front ofthe wafer surface, and it can be seen that they both end up at the samepoint in the detector plane. This is because the optics were selected sothat an image of the source, S would be recreated in the plane of thedetector, after reflection from the front surface of the wafer. In thisexample, this meant that the focal length of L1 was chosen to match thedistance between S and L1, and the focal length of L2 matched thedistance between L2 and the front surface of the wafer, and the focallength of lens L3 matched the distance between L3 and the detector D2.

The condition that the source, S, is imaged onto the detector plane viareflection from the front surface of the wafer, WF, ensures that theenergy from the source is efficiently transferred to a small region ofthe detector plane, where detector D2 is located. In the embodimentshown in FIG. 7, the two rays ARF and BRF converge to the same point ondetector D2, because they originate from the same point on source S. Inthis embodiment, that point on source S is on the optical axis, but thesame would be true for any point in the plane of S. The rays that arereflected from the back of the wafer BTRB and ATRB, on the other hand,reach the plane of detector D2 at different locations. If desired, theycan be detected with detectors D1 and D3. As described above, the raysthat are reflected from the back of the wafer BTRB and ATRB can alsoprovide useful information regarding the optical characteristics of thesubstrate. Thus, in certain embodiments, one may only be interested indetecting the rays that are reflected off the front of the substrate,while in other embodiments one may only be interested in detecting therays being reflected off of the back of the substrate. Of course, instill other embodiments, the rays being reflected off the front of thesubstrate and the rays being reflected off the back of the substrate mayeach be individually measured.

Another optical pathway that may be used in accordance with the methodof the present invention is shown in FIG. 8. The optical pathwayillustrated in FIG. 8 is similar to the optical pathway illustrated inFIG. 7. In this embodiment, however, the two rays A and B are emittedfrom the source S at different angles to the optical axis. Once againthe rays that were reflected from the front surface of the wafer, ARFand BRF arrive at the same point on the detector D2. However the tworays reflected from the back of the wafer ATRB and BTRB, arrive atdifferent locations, and only BTRB lands on the detector D2. Thisillustrates as a general point about the relative impact of raysreflected from the front of the wafer or the back of the wafer on thesignal detected by detector D2. The energy that is reflected from theback surface of the wafer, WB, may end up being distributed over alarger area in the plane of the detector than the energy reflected fromthe front of the wafer WF. As a result, the relative contribution ofenergy reflected from the back of the wafer to the signal from thedetector D2 is smaller than that from the reflection from the front ofthe wafer. The reason for this is because the optics were selected sothat an image of the wafer surface WF is formed at the plane of thedetector. Since the rays reflected from the back of the wafer WB are notimaged at the detector plane, the distribution of energy is more spreadout.

This principle of discriminating between the energy reflected from theback of the wafer and that from the front of the wafer by selecting theoptical conditions to optimize the energy density landing on thedetector is illustrated in FIG. 9. The curve A illustrates the powerdensity distribution in the plane of the detector for light that hasbeen reflected from the front surface of the wafer. Curve B shows thecorresponding distribution for light that has been reflected from theback of the wafer. Curve C, is that for light that has undergone morethan one reflection at the back surface, and curve D is the intensitysum from curves A, B and C. If we consider that portion of lightrepresented by curve D that falls between the axis positions −XD/2 and+XD/2 as being the energy detected by a detector, we can see that thecontribution of signal from curve A is much larger than that from curveB or C.

As shown in FIGS. 6-8, various optical pathways may be used and adjustedin order to separate the different light components and/or to otherwisecontrol the contribution of the light signal from the front reflectionor the back reflection. Further, other techniques and optical elementsmay be added to the optical pathway for facilitating separation of thedifferent components. For example, apertures or light filters may beincorporated into the optical pathway for blocking light where desired.

For example, referring to FIG. 10, one embodiment of an optical pathwaythat uses a blocking element 70 is shown. In this embodiment, theblocking element 70 is used to block light ray B and rays with smallerinclinations to the axis. In this manner, the detector D2 only receivesrays that have been reflected from the front surface WF of thesemiconductor wafer.

Such blocking elements, that control the distribution of angles ofincidence at the wafer surface may also be positioned elsewhere, eitherin the incident beam or in the reflected beam, so long as their effectis to block those rays that have been reflected from the back of thewafer and are still capable of landing on the detector of interest.Control of the distribution of angles of incidence may also be useful ifit is desirable to match the measured reflectance to a specific angle ofincidence or range of angles of incidence. In some embodiments, it isalso possible to vary the range of angles of incidence by an adjustableblocking element and take measurements of the reflected light signal atdifferent settings. These kinds of measurements can assist incharacterizing the optical properties of the sample, for example bycharacterizing the degree of absorption within the wafer.

Optical pathways made in accordance with the present invention mayinclude a single blocking element 70 as shown in FIG. 10 or multipleblocking elements depending upon the particular application. It shouldbe understood that a blocking element may be included in the opticalpathway as a separate component as shown in FIG. 10 or may beincorporated into one of the other optical elements. For example, thelimited diameter of a lens, mirror, or other optical element can act asa blocking element as used herein, when these elements can limit thespatial extent of rays that propagate through the optical system andreach the detector.

The blocking element 70 can be any suitable device capable ofeliminating any unwanted rays of light. In one embodiment, for instance,the blocking element may comprise a device that includes an aperture foronly allowing selected light rays to pass. As described above, however,a lens, filter, mirror or other optical element may also be used.

Another approach for controlling the ratio of the energy reflected fromthe front surface WF to that reflected from the back surface WB involvesoptimizing the focal lengths of the lenses, especially lenses L2 and L3.The ratio of the focal lengths of these lenses controls themagnification of the intermediate image of S that is formed at the frontsurface WF when it is reimaged at the detector plane D2. By decreasingthe focal length of lens L2 relative to that of lens L3, themagnification can be increased. This has the effect of increasing theability to discriminate between reflection from the front and the back.FIG. 11 illustrates the point, since in this case we see that ray BTRBno longer falls on the detector D2, showing improved discriminationagainst light reflected from the back of the wafer as compared to theexample in FIG. 8 where BTRB lands on the detector.

In one embodiment, as shown in FIG. 11, the different light componentscan be separated out by decreasing the depth of focus. In theembodiments shown in FIGS. 7and 8, the front of the wafer, WF is at thefocal point of lens L2, and the detector is at the focal point of L3.The depth of focus of L2 depends on a number of factors including thefocal length and the angle of the illumination. If the conditions areset so that lens L2 and lens L3 only form an image at the detector planefor the set of rays that predominantly emanate from a narrow range ofpositions around the surface WF, then the depth of focus is limited to aregion near the surface of the wafer. By ensuring that the back of thewafer WB lies outside the depth of focus, the rays reflected from thefront and the back of the wafer may be separated, because the majorityof radiation that reaches the detector has been reflected from the topsurface of the wafer.

In some embodiments, a relatively large range of angles of incidence inthe incident beam may be used. This condition may also be morerepresentative of the range of angles-of-incidence for the heatingradiation incident on the wafer within the process chamber, providing asecond benefit of this measurement approach. In this manner, one canevaluate the way in which the heating radiation impinges on the wafer inthe chamber by optical modeling, for example by the use of ray-tracingsoftware. A proper understanding of the range of angles of incidence ofthe heating radiation can then be used to match the illuminationconditions used within the measurement system to those that apply in theprocessing equipment.

In some cases, the reflected light can be collected from a rather smallregion on the wafer surface, to prevent the collection of light that haspropagated to the back surface of the wafer and been re-reflected towardthe surface. The size of the region from which reflected light iscollected is determined by the optics used, the size of the detector andany apertures, filters or other optical elements included. The optimalsize for the area analyzed partly depends on the thickness of thesample, since if the sample is very thin it is more difficult toseparate rays from front and rear surface reflections if light isselected from a large area on the wafer surface. However, there may beother factors to consider. For example, if a surface of the wafer ispatterned, then the reflectivity may vary within the region from whichreflected light is collected. This may be advantageous if it desired tocollect average properties of the region.

For instance, in one embodiment, the size of the region on the wafersurface from which the reflected light is collected can be relativelysmall and can be designed to match an area viewed by a temperaturemeasuring device, such as a pyrometer. In other words, the field of viewof the pyrometer can match the area from which the reflected light iscollected. In other embodiments, however, light can be collected from arelatively large region on the wafer surface. Collecting reflected lightdata from a relatively large area may be useful when optimizing powercoupling between a heating device and the substrate. On the other hand,if the substrate is being heated by an energy beam, the area that isoptically characterized can be matched to the area irradiated by theenergy beam. Such an approach may be especially useful forcharacterizing and optimizing coupling of energy from laser beams. Thiscould be especially useful for lasers that emit energy at wavelengthsgreater than ˜1 μm, where semiconductor substrates are frequentlysemi-transparent. For example, such lasers include diode lasers, YAGlasers, fiber lasers, CO and CO₂ lasers.

In one particular embodiment, the light source may be scanned across thesubstrate. Information can then be sequentially collected about thereflected light intensity. Scanning may occur by moving a light source,moving the optical pathway, and/or by moving the substrate itself. Inthis manner, information can be collected at any particular location onthe substrate. Alternatively, an average may be collected across thearea of the wafer.

In one embodiment, a microscope objective lens may be used in order toprovide a short focal length lens. The lens may be placed anywhere inthe optical pathway, such as at the lens L2 as shown in FIG. 11. Whenpositioned at lens L2, the microscope objective lens may be used tofocus the radiation onto the wafer surface. Such lenses can have smallfocal lengths and high numerical apertures. As a result they provide aconvenient approach for providing an optical system that illuminates thewafer with a large range of angles of incidence and collects light witha small depth of focus, especially when the resulting magnification ofthe wafer surface is relatively large (e.g. the optical system has amagnification greater than ×10, such as greater than ×50). However manyalternative approaches can be considered, including optics that arelarger and further from the wafer surface, so long as it is ensured thatthe light is collected only from the desired region and that themajority of the collected radiation has only been reflected at the firstsurface. The optical axis of the measurement system also need not benormal to the wafer surface.

Analysis of the distribution of light in the plane of the detector ispossible by scanning a detector in this plane, or through the use ofvarious sizes of detector, or variable or scanning apertures in theplane of the detector, or by employing an imaging detector such as acharge-coupled device (CCD) camera, or an array of detectors. Theinformation about the spatial distribution of the light at the plane ofthe detector can be used to refine the measurements. For example, if thethickness of the substrate is known or if it is measured, then it ispossible to interpret the shape of the intensity distribution withrespect to components that are reflected from the front surface or theback surface of the wafer. An algorithm can be used to split thedetected distribution into a component that is reflected from the frontsurface, as opposed to other components that originate from multiplereflections within the substrate. Hence, as suggested in FIG. 9,components reflected from the back surface can be mathematicallysubtracted from the total signal, to yield a more accurate estimate ofthe signal reflected from the front surface of the wafer.

In FIGS. 5-8 and 10-11, the focus has primarily been on differentiatingthe amount of light reflected from the front surface of the wafer asopposed to light reflected from the back surface. As mentioned above,there is actually an infinite series of reflected rays. FIG. 12illustrates how a single ray, A, from the source S propagates throughthe optical system described before. In this case the figure shows thepath of the ray R1, that is reflected from the front of the wafer, WF,ray R2, which arises from one reflection at the back surface WB, as wellas R3, R4 and R5, which arise from two, three and four reflections atthe back surface, respectively. In principle there an infinite numberrays in the series, but as mentioned above, the intensity of raysdecreases rather quickly because of energy losses. The rays R1, R2, R3,R4 and R5 arrive at detectors D2, D3, D4, D5, and D6 respectively. It ispossible to measure the intensities of each of these rays in order tobetter characterize the optical properties of the wafer. When it isdesirable to measure the rays R1, R2, R3, R4 and R5, for instance, thelight source S may be a laser source in order to generate a sufficientintensity for the measurements to occur.

For a source emitting rays across a range of angles of incidence therewill be many rays falling on each of the detector elements, leading to afamily of curves such as B & C shown in FIG. 9. Analysis of thedistribution of intensities may help to identify the components asdescribed above, and such approaches can be combined with the use ofapertures or other optical elements that can restrict the range ofangles that propagate and hence the families of reflected lightcomponents that can reach the detector.

The principles described with respect to analysis of reflected light canalso be applied to analysis of the light transmitted through thesubstrate. FIG. 13, for instance, shows one embodiment of two rays A andB propagating from a source S through an optical pathway, where lensesL1 and L2 serve much as before to form an image of a light source S atthe wafer surface, WF, and lenses L4 and L5 reimage the image of S at WFto the plane of a detector TD2. The design ensures that the transmittedrays that are not reflected from the back of the wafer, TA and TB, arebrought to focus at the plane of TD2. The rays that have undergone atleast one reflection at the back surface of the wafer, such as ATRBRFand BTRBRF arrive at different locations in the plane of the detector.Hence in a manner rather analogous to that for the reflected rays, it ispossible to decrease the contribution of multiply reflected rays to thesignal detected by TD2.

FIG. 14 shows the behavior of a single ray A, that is transmittedthrough the optical system and the wafer, generating multipletransmitted rays, in a fashion rather analogous to that of the multiplyreflected rays illustrated in FIG. 12. Such rays may also be detected byan array of detectors if desired, and similar analysis methods used toanalyze the spatial distribution of transmitted light to those discussedin the context of the spatial distribution of reflected light.

It should be noted that although the illustrations here show the use oftwo lenses between the source and the wafer, the general principles canbe achieved with a wide variety of alternative optical pathways usingeither more or fewer lenses, or indeed by substituting mirrors, such ascurved mirrors or other optical elements for some or all of the lenses.Optics that control the state of polarization of the incident orreflected light can also be included in the apparatus if needed. Suchoptics can include polarizers and retarders, such as quarter, half orfull wave-plates, or other optical elements that can produce radiationof a desired state of polarization, including plane polarization,elliptical or circular polarization.

When configuring the state of polarization and/or configuring the angleof incidence, it should be noted that these factors should be taken intoaccount for any given measurement arrangement. For normal incidence andnear-normal incidence (e.g., light which is incident at angles ofincidence less than about 25°) the effects are usually quite small. Inthe case of non-normal incidence, it is often useful to performmeasurements with the incident radiation polarized in either the s-planeor p-plane. Measurements for both conditions can allow for a fulldetermination of the optical properties of the substrate. Ellipsometricmeasurements may also be performed at various times, such as during lowtemperature pre-characterization of the substrate.

The measurements can be made at any wavelength of interest, or they canbe performed across a spectrum, through the attachment of appropriatespectrocopic apparatus such as a monochromator or otherwavelength-selective filtering elements. Measurements of integratedproperties can also be performed by using a broad-band energy source andcollecting all the radiation reflected at a detector with a broadwavelength response.

The light source S that is used to emit light onto the semiconductorwafer can be any suitable light emitting device. The light source, forinstance, may emit light at a range of wavelengths or at a specificwavelength. Suitable light sources may include W-halogen light bulbs,Xe-arc lamps, discharge lamps, light emitting diodes, lasers, or thermalsources such as black-body cavities, glowbars or other thermal radiationemitting elements. In some cases it would be useful to set the lampradiation sources at so that they emit spectra representative of theenergy source used in the processing apparatus. One way to do this is tocharacterize the radiation source of interest and combine it withwavelength filtering elements that can mimic the energy source in theprocessing equipment.

In one embodiment, the light source may comprise a super-continuum lightsource. A super-continuum light source possesses some special advantagesfor rapid measurement of wafer optical properties, since it is farbrighter than a conventional broad-band light source such as atungsten-halogen lamp or an LED. This can be useful for performing veryfast measurements, since the energy delivered in a given time is muchlarger, allowing higher signal levels for detection of reflected,transmitted or scattered light. It can also be useful if there is arelatively high level of stray background radiation that may interferewith accurate measurement of wafer properties, since a very brightillumination can make light from such stray light sources insignificantas compared to that from the super-continuum light source. This can havespecial advantages for measurements of optical or thermal properties ofa wafer in a processing chamber, especially if the wafer is hot or ifthere is stray radiation being emitted by heating elements, lamps,lasers or plasma. A very bright radiation source also allows the use ofcompact optics, since a large amount of radiation may be delivered froma small emitting area and it can be conveniently coupled tofibre-optics, light pipes and other elements that can be convenientlyintroduced into a processing equipment and chambers. The super-continuumlight source can also produce a spectrum that is relatively flat, i.e.that does not vary by a great deal over a wide wavelength range. Thishas the advantage of extending the wavelength range that is convenientlycovered by the light source and simplifying the interpretation ofspectral measurements such as reflection and transmission spectra.

The super-continuum light is generated by exposing a non-linear mediumto high power radiation. For example it can be generated by applying ahigh power pulse of radiation from a laser to a water cell andcollecting the spectrum of emitted light. An efficient approach involvesusing a photonic crystal fibres or tapered fibres. Super-continuum lightsources can generate spectra of light covering wavelength ranges thatare useful for characterizing semiconductor wafers. For example, theKOHERAS SuperK™ White super-continuum source from KOHERAS A/S (Birkerød,Denmark) produces a spectrum of radiation with a power spectraldensity >4 mW/nm between 460 nm and 2000 nm. Such light sources can beof special interest for measuring wafer transmission or reflectionwithin the process chamber. The measurements can be used to deduce thetemperature of the wafer. Furthermore, the light source may be used fora variety of other measurements, either directly or in combination withwavelength-selective filtering elements. Such elements can select thewavelengths of light delivered to the wafer, or light that is collectedfrom the wafer after reflection, scattering, transmission or emissionfrom the wafer. Measurements can include reflection and transmission asmentioned above, but they can also include methods where the lightreaching the wafer is modulated and it creates a thermal or electronicmodulation of the wafer's properties. Such a modulation can be detectedand used to extract information about the wafer.

Furthermore, such light sources may even be useful for thermalprocessing, especially for the case where the wafer has a pattern ofcoatings on it. In this case, the use of a broad spectrum for heatingcan reduce the degree of variation in the power absorbed by differentregions of the pattern, hence providing more uniform processing.

When thermal energy sources are used, it may be useful to set theirtemperatures to be representative of the wafer temperature under thereal processing conditions. If necessary the latter could be set tomatch the wafer temperature on a recipe-by-recipe basis. For example ifthe key process step occurs at 1000° C., then the thermal source may beat that temperature. For these cases, where broadband radiation sourcesare used, it can be convenient to use a broadband detector such as athermopile, a bolometer or a pyroelectric device to detect the reflectedradiation. Differences between the conditions that apply within theprocessing chamber and within the measurement apparatus can becompensated for by calibration procedures. If the processing equipmentuses a laser for heating the wafer, it may be necessary to make theoptical measurement at the same wavelength. If the laser is incident onthe wafer at a specific angle of incidence and polarization state thoseaspects may also be incorporated in the measurement.

It should be understood, that measurements on both the front surface andthe back surface of the substrate may be performed to provide a morecomplete description of the optical properties of the substrate. Asdescribed above, in one embodiment, the measurements may also be takenat a number of positions across the surface of the wafer. Thisinformation may then provide a map of the spatial distribution ofradiative properties across the wafer.

Taking measurements at multiple locations across the wafer's surface maybe especially valuable for improving the uniformity of processing, forexample by improving temperature uniformity. For instance, theinformation about the variation of optical or thermal properties acrossthe wafer's surfaces could be provided to the measurement and controlsystems. In one embodiment, the information can be used by a model-basedcontroller in order to predict how to optimize the heating conditions atdifferent locations on the wafer. For example, the distribution ofproperties can be provided to a model-based control system that predictsoptimized settings for power provided to different banks of lamps so asto optimize temperature uniformity. Similar methods can also be used tocontrol power coupling variations when heating or otherwise subjectingthe substrate to one or more laser beams.

Information about the variation of optical properties across the surfacemay be useful for correcting the readings of sensors that sensetemperature at different locations on the wafer. Information aboutvariations in the thickness or the doping of the wafer may also be usedfor similar purposes. Likewise, information about variations in thecoatings or patterns on the wafers can be used in a similar manner.

In some cases it may be useful to perform the measurements in at leasttwo configurations, one where the reflected light is only collected fromthe illuminated surface, and one where the optical configuration so thatthe depth of focus is large and light is collected after reflection atboth surfaces of the wafer (as in the case shown in FIG. 3). These twocases could be accommodated by changing the depth of focus within oneoptical pathway, for example through the use of an aperture as shown inFIG. 10 or through separate measurement steps.

The combination of reflectivity measurements from both surfaces of thewafer, and a wafer transmission measurement allows a rather completecharacterization of optical properties. One useful aspect oftransmissivity or reflectivity measurements performed at roomtemperature are that they allow for determination of whether the waferis heavily-doped or not. This can be ascertained by deducing the degreeof optical absorption at wavelengths greater than ˜1 μm. If theabsorption coefficient is significantly greater than that expected forlightly-doped material, such as silicon of a resistivity of more than0.5 Ωcm, then the material can be identified as heavily doped. Thisinformation can then be used to improve temperature measurement accuracyand to improve the temperature control, especially during processing attemperatures below ˜800° C.

Performing premeasurements at more than one temperature, for instance,can be used to distinguish lightly-doped wafers from heavily-dopedwafers, or in general to provide information about the nature of thedoping. Taking measurements at more than one temperature, may also beuseful in determining other properties of the wafer. For instance, themeasurements at different temperatures, in conjunction with the sensingof surface reflectivities, may show temperature dependence in thesurface reflectivities. That information can be useful for improving theaccuracy of the estimates of the temperature dependence of reflectance,transmittance, emittance, or absorptance. For example, thereflectivities of the surfaces at the temperatures of interest (T2) canbe obtained by extrapolating from the measurements obtained at othertemperatures, such as T1 and T3. The concept of characterizing at morethan one temperature and extrapolating to a third temperature may alsobe useful for estimating the temperature dependence of the absorptioncoefficient of the substrate.

Any of these measurements can be combined with an approach thatmodulates the light transmission through the substrate, for examplethrough the illumination that introduces extra free carrier absorption,for example, by creating extra electron-hole pairs in the semiconductor.Modulation of the degree of absorption will manifest itself through acorresponding modulation in components of the reflected or transmittedradiation that are sensitive to propagation of rays through thethickness of the substrate. This approach may be useful in improvingaccuracy. We can also modulate the light transmission by applying otherforms of radiation, including electron irradiation, which could beconveniently obtained by mechanical modulation of a flux of betaparticles from a beta-radiation emitter. It may also be possible toobtain extra information by deliberately modulating the wafertemperature and observing changes in the measured properties.

As described above, the wafer surfaces may scatter radiation as a resultof patterning or variations in surface topography. In such cases, theintensity of the beams of reflected and transmitted light may beaffected by the scattering pattern. One way of characterizing thepresence and degree of scattered light is to examine whether thetransmittance measured for light incident on either surface of the waferis the same. If it is different depending on the surface illuminated,then it is likely that at least one of the wafer surfaces is scatteringlight in directions that are not correctly collected for thetransmittance measurement. Hence measurement of an asymmetrictransmittance can be a symptom of light scattering. Characterization ofthe light scattering pattern of the wafer can help to improve accuracyof predictions of optical properties. This can be especially helpful inproviding improved estimates of spectral emittance at a pyrometerwavelength. In some cases, where the effects of light scattering areespecially significant, it may be necessary to measure the bidirectionalreflectance distribution function of the wafer to make an accurateestimate of the spectral emittance. It can also be helpful to useintegrating spheres to control the illumination conditions formeasurements of reflectance and transmittance.

When characterizing the interaction between the wafer and any givenheating energy source, the calculation often requires the spectraldistribution of the energy emitted by the energy source to be taken intoaccount. This aspect can be covered by measuring the optical propertiesof interest as a function of wavelength, over a wavelength interval thatcovers the spectral region where the energy source emits its energy. Aweighted integral of the optical property can then be used to obtain theintegrated property. For example, if the property of interest is aquantity f(λ,T), and the energy source emits a spectrum I_(L)(λ), thenthe integrated property is F(T), where${F(T)} = {\frac{\int{{I_{L}(\lambda)}{f\left( {\lambda,T} \right)}{\mathbb{d}\lambda}}}{\int{{I_{L}\left( {\lambda,T} \right)}{\mathbb{d}\lambda}}}.}$The integrals are performed over a wavelength range that includes mostof the energy emitted by the heating source. The quantity f(λ,T) couldbe the reflectance, absorptance, transmittance etc. For determination ofpower coupling to an energy source, the integrated absorptance is ofspecial interest. Similar principles can be applied to determining theintegrated emittance, such as the total emittance. In this case, theweighting spectrum is the black-body radiation spectrum for thetemperature of interest. For example, the total emittance, ε_(tot)(T)can be calculated from the spectral emittance, ε(λ,T) according to theequation${{ɛ_{tot}(T)} = \frac{\int{{W_{bb}\left( {\lambda,T} \right)}{ɛ\left( {\lambda,T} \right)}{\mathbb{d}\lambda}}}{\int{{W_{bb}\left( {\lambda,T} \right)}{\mathbb{d}\lambda}}}},$where W_(bb)(λ,T) is the Planck radiation function that describes theemission spectrum of a black-body radiator. The integrals are performedover a wavelength range that includes most of the energy emitted by ablackbody radiator at temperature T. Estimates of integrated emittancecan be used to help determine the degree of heat radiated away from thewafer when it is at any given temperature. An alternative approach fordetermining integrated properties can involve illuminating the waferwith an appropriate spectrum and hence directly performing an integratedmeasurement. The latter approach may require a careful tailoring of theillumination spectrum and the spectral response of the optical detectionsystem, but may have the advantage of being faster and simpler in somecases.

As described above, in one embodiment, measurements may be taken on boththe front surface and the back surface of the substrate in order toprovide a more complete description of the optical properties of thesubstrate. In still another embodiment, both sides of the wafer may beboth illuminated for taking dual-sided measurements.

For example, FIG. 15 shows the arrangement where the apparatus includesthe capability to provide light that is incident on either of thewafer's two surfaces. Radiation source SWF illuminates the front side ofthe wafer (WF). Light that is reflected from WF is collected by DRWF,which is a radiation collection and sensing arrangement. DRWF caninclude optics that limit the radiation that is sensed to being onlythat component that is reflected from WF, if desired. Likewise DTWF is aradiation collection and sensing arrangement that collects radiationtransmitted through the wafer. Radiation source SWB illuminates the backside of the wafer (WB). Light that is reflected from WB is collected byDRWB, which is a radiation collection and sensing arrangement. DRWB caninclude optics that limit the radiation that is sensed to being onlythat component that is reflected from WB, if desired. Likewise DTWB is aradiation collection and sensing arrangement that collects radiationtransmitted through the wafer. The combination of these measuringsub-systems allows measurements with illumination from either side ofthe wafer for a more complete characterization of the wafer'sproperties.

FIG. 16 shows a second arrangement where the apparatus includes thecapability to provide light that is incident on either of the wafer'stwo surfaces. Radiation source SWF illuminates the front side of thewafer (WF). Light from SWF that is reflected from WF is collected by D1,which is a radiation collection and sensing arrangement. D1 can includeoptics that limit the radiation that is sensed to being only thatcomponent that is reflected from WF, if desired. Likewise D2 is aradiation collection and sensing arrangement that collects radiationfrom SWF that is transmitted through the wafer. Radiation source SWBilluminates the back side of the wafer (WB). In this arrangement theoptics are configured so that light from SWB that is reflected from WBis collected by D2. D2 can include optics that limit the radiation thatis sensed to being only that component that is reflected from WB, ifdesired. Likewise D1 can collect radiation from SWB that is transmittedthrough the wafer. This embodiment can perform the same measurements asthose possible with FIG. 15, but this embodiment uses less opticalcomponents and detectors and hence would be cheaper and simpler. It alsomay be easier to perform the measurements at the same spatial locationon the wafer with the scheme in FIG. 16. If desired, the measurementsusing radiation from SWF and from SWB can be performed at differenttimes, to prevent radiation from SWF reaching the sensors at the sametime as they are sensing radiation from SWB. Alternatively themeasurements can be separated by using modulation of the radiationoutput from at least one of SWF or SWB to provide a time-varyingcharacteristic to at least one of the signals that allows it to bedistinguished as arising from radiation from a particular light source.For example, the output of SWF can be intensity modulated at a knownfrequency and the signals from D1 and D2 can be filtered to track thebehavior of that frequency component. Other methods of separating thesignals can include exploitation of differences in the light output fromSWF and SWB, such as wavelength or state of polarization. It is alsopossible for the characteristics of the light collection and sensingarrangements D1 and D2 to be varied so that they are more appropriatefor the measurement of radiation from SWF or from SWB. For example, thecharacteristics of D1 may be set to optimize the collection of reflectedlight while it is collecting light from SWF that is reflected from thewafer, and then they may be set to optimize the collection oftransmitted light when it is collecting light that is transmitted fromSWB. Of course, the characteristics may be optimized to perform both ofthese function simultaneously if so desired.

Characteristics of the light collection and sensing arrangements shownin FIGS. 15 and 16 that can be optimized for measurement of waferproperties can include adjustment or selection of the position or shapeof optical elements such as lenses, apertures, mirrors and detectors.They can also include adjustment of filtering or polarizing elements.They can also include such as electronic or digital filters, amplifiersettings and signal processing circuits and algorithms. The radiationsources SWF and SWB can also include optical and electronic elementsthat assist in optimizing the measurement of components of reflected ortransmitted light, and these elements can be varied for measurement ofspecific wafer properties if desired. Although the configurations shownin FIG. 15 and FIG. 16 show light incident at an angle to the normal ofthe wafer, the measurements may also be made at or near normal incidenceif desired. In such cases it is convenient to include beam-splittingoptics that allow the light collection and sensing arrangements tosample radiation reflected or transmitted by the wafer while notcompletely blocking the path of the incident radiation.

For many applications it is useful to make the optics that deliverradiation to the wafer or that collect radiation reflected from ortransmitted by the wafer achromatic. Such optics have the characteristicthat their focusing properties do not vary significantly withwavelength. This allows the measurements to be performed over a broadrange of wavelength (either sequentially or simultaneously) whilesampling radiation from the same region of the wafer. An achromaticapproach is most easily achieved through the use of reflective optics.

FIG. 17 shows an example of an apparatus where the measurements areperformed at more than one location on the wafer. In this example, thelight is incident on the front surface of the wafer, but the approach iseasily extended to measurements with light incident on the back surfaceof the wafer, or to the approaches of FIGS. 16 and 17, where dual-sidedmeasurements are possible. Measurements at several locations or evenmapping of the wafer's properties are also possible by other schemes.For example, the wafer can be mechanically moved past a measuringarrangement, so that properties can be evaluated at different locations.Alternatively, the measuring apparatus can be moved relative to astationary wafer, or the beams of radiation used for measurement can bescanned over the surface of the wafer. Another approach would involveilluminating the whole wafer, or at least a fraction of the wafer, witha broader beam of radiation and analyzing the reflected and transmittedbeams of radiation. The beam can contain light reflected from the wholeof the wafer, or from a sub-region, such as a line-shaped region. Suchanalysis can be performed by scanning radiation collecting and sensingarrangements with respect to the beams of radiation, or scanning thebeams of radiation relative to the collecting and sensing arrangement.Alternatively, the beams of light can be collected by optical systemsand delivered to imaging devices, such as cameras.

Practical Applications of the Above Described Methods

Once we have obtained measurements of the surface reflectivities, and ifdesired the wafer transmissivity, this information can then be used topredict the thermal radiative properties of the wafer during waferprocessing. A very simple approach could be applied for processesconducted at wafer temperatures T>700° C. In this case, for mostconsiderations, silicon wafers that are >600 μm thick can be consideredto be opaque at all wavelengths of interest. If this is the case, thereflectivity and the wafer emissivity at any given wavelength can berelated by Kirchhoff's law.

A more sophisticated approach would incorporate information about thewafer's temperature to make an improved estimate of the radiativeproperties. For example, if a pyrometer reading is available then thetemperature deduced from this can be used to improve estimates ofproperties in various ways. One approach would be to predict theabsorption coefficient of the wafer from a model, and then combine thisproperty with the room temperature measurements of optical properties ofthe wafer to provide a more accurate estimate of the high-temperatureproperties of the wafer.

The pyrometer reading could also be used to provide a better estimate ofthe radiation loss from the wafer. The loss depends on both theradiative properties and the temperature. By combining estimates of thetwo properties, an improved estimate of the radiative heat loss fromvarious regions of the wafer can be obtained, and hence the wafertemperature control and temperature uniformity can be improved by makingsuitable adjustments to the lamp powers.

For example, the following are more detailed methods for using theinformation collected from the optical pathways illustrated in thefigures. As mentioned above, in one embodiment, the present disclosureis directed to a method of correcting the readings of a radiationsensing device, such as a pyrometer, at high temperature where theinternal transmittance of the substrate is less than 0.1. In thisembodiment, the optical pathway of the present invention is used tocollect light reflected from one surface of the wafer, such as the frontsurface of the wafer. The measurements are taken while the wafer is at arelatively low temperature, such as at ambient temperature. Themeasurements are also performed at substantially the same wavelengthrange at which the pyrometer operates.

From the method of the present disclosure, the reflectivity of the frontsurface of the wafer is determined. This reflectivity is used to deduceor determine reflectance of the wafer at high temperature. Specifically,at high temperature, reflectance is substantially the same asreflectivity of the front surface due to the decrease of internaltransmittance with temperature. From the reflectance, the emittance ofthe wafer may be determined. For example, the emittance is generallyequal to 1 minus the reflectance. The determined emittance is then usedto correct pyrometer readings and improve the accuracy of temperaturecontrol.

In an alternative embodiment, the methods of the present invention canalso be used to correct for pyrometer readings at lower temperatureswhere the internal transmittance of the substrate is greater than 0.1.In this embodiment, the optical arrangement as shown in the figures maybe used to collect and determine the amount of light reflected from onesurface of the wafer while the wafer is at a relatively low temperatureand at the wavelength range at which the pyrometer operates.

In this embodiment, the optical arrangement of the present disclosuremay also be used to collect light reflected from the opposite surface ofthe wafer, such as the back surface of the wafer using the sameconditions as above. From this information, the reflectivity of thefront surface of the wafer and the reflectivity of the back surface ofthe wafer may be determined. Transmittance of the wafer may then bemeasured or may be determined from a model or other measurement of thewafer at higher temperature.

After the transmittance is determined, the emittance of the wafer can bedetermined. For instance, the emittance is generally equal to 1 minusthe transmittance minus the reflectance. This emittance can then be usedto correct pyrometer readings and improve the accuracy of temperaturecontrol.

In addition to providing improved temperature measurements, the methodsof the present disclosure can also be used to control the heatingdevices in order to optimize power absorption. For example, at highertemperatures where the internal transmittance of the wafer is less than0.1, the methods of the present disclosure can be used to collect anddetermine the amount of light reflected from one surface, such as thefront surface of the wafer. These measurements may be completed at lowtemperatures, such as at or near ambient temperature. In thisembodiment, however, the wavelength range at which the measurements aretaken should substantially overlap with the wavelength range for theheating device that is used to heat the wafer during processing.

Once the reflectivity of one surface of the wafer is determined, thereflectivity is used to determine reflectance at higher temperatures. Asmentioned above, at higher temperatures, reflectance is substantiallyequal to the reflectivity, due to the decrease of internaltransmittance.

The reflectance can then be used to determine absorptance, which isgenerally equal to emittance at higher temperatures. In particular,absorptance equals 1 minus the reflectance. The absorptance can then beused to optimize power absorption and/or the energy setting for one ormore heating devices contained in the chamber.

The above method is particularly well suited for systems such as thoseshown in FIG. 1 where the wafer 14 is heated by the heating device 22from one side of the wafer. If both sides of the wafer are heated byseparate heating devices, however, the above method can be repeated forthe opposite surface of the wafer. In this manner, a first heatingdevice heating the top of the wafer may be controlled independently of asecond heating device heating the bottom of the wafer.

The methods of the present disclosure can also be used to optimize thesettings of the heating device at lower temperatures where the internaltransmittance of the substrate is greater than 0.1. In this embodiment,an optical arrangement is used to collect light reflected from onesurface of the wafer at or near ambient temperature and at a wavelengthrange that substantially overlaps with the wavelength range of theheating device that heats the wafer. The same measurement determinationsare then carried out on the opposite surface of the wafer at similarconditions.

From this information, the reflectivity of the front surface and thereflectivity of the back surface of the substrate may be determined.Transmittance of the substrate is then measured or deduced from a modelof the wafer at higher temperatures. Once transmittance is determined,the absorptance may be estimated by assuming that the absorptance issubstantially equal to the emittance. Therefore, the absorptance isequal to 1 minus transmittance minus reflectance based on one side ofthe wafer. The absorptance is then used to optimize power output overthe heating device and/or the energy setting of the heating deviceduring wafer processing.

Again, if a first heating device heats one side of the wafer and asecond heating device heats an opposite side of the wafer, the abovemethod can be repeated for the opposite surface of the wafer foroptimizing both of the heating devices independently of one another.

In addition to the above embodiments, the information obtained frommethods of the present disclosure can be used to control various otherparameters contained within the thermal processing chamber.

Although the optical characteristic of the substrate as described abovemay be determined within the thermal processing chamber 10 as shown inFIG. 10, in one embodiment, the optical characteristics may bedetermined at a different location, such as on any suitable platform, ona robotic arm or in a separate chamber. In addition, the abovemeasurements may occur immediately prior to processing or at a differenttime to the wafer processing itself. For example, referring to FIG. 2,an entire wafer processing system is illustrated. In this embodiment, aplurality of wafers are stacked in a cartridge 100 that is placed inclose proximity to the thermal processing chamber 10 and a wafer opticalprocessing chamber 200 made in accordance with the present invention. Inorder to move the wafers from one location to another, the systemfurther includes a wafer handling device 110.

During processing, wafers contained in the cartridge 100 may be moved tothe wafer optical processing chamber 200 in order to determine at leastone optical characteristic of the wafer in accordance with the methodsdescribed above. Once the wafer characteristics are determined, thewafer is then transferred to the thermal processing chamber 10 onceagain using the wafer handling device 110. The optical characteristicsof the wafer that are determined in the wafer optical processing chamber200 may then be used to control at least one process variable or systemcomponent in the thermal processing chamber 10. For example, theinformation may be used to control a power controller for the heatingdevice or may be used to calibrate or otherwise control a pyrometer usedto determine the temperature of the wafer during processing.

Referring back to FIG. 1, the thermal processing system 10 may furtherinclude a system controller 50 which can be, for instance, amicroprocessor. Controller 50 can be configured to receive voltagesignals from the light detectors 30 that represent the radiation amountsbeing sampled at the various locations. Controller 50 may be configuredto calculate the temperature of the wafer 14 based upon the amount ofradiation sensed from the light detectors 30 in conjunction with theoptical characteristics that are determined in the wafer opticalprocessing chamber 200.

The system controller 50 as shown in FIG. 1 can also be in communicationwith the heating device power controller 25. Again, based upon theoptical characteristics of the wafer that are determined outside of thechamber, the controller 50 can selectively increase or decrease thepower to the heating device for optimizing absorption of thermal energybeing emitted by the heating device and being absorbed by the wafer 14.In addition to controlling radiation intensity, however, it should beunderstood that the power controller 25 in conjunction with the systemcontroller 50 may be used to control the heating device 22 in otherways. For instance, the system controller 50 may also be configured tochange the amount of radiation being emitted by the lamps 24 such thatdifferent portions of the surface of the wafer are subjected todifferent amounts of radiation. The angle of incidence at which theradiation contacts the wafer 14 and the wavelength of the radiation mayalso be selectively controlled in accordance with the present invention.

Prior to a further detailed discussion of various particular methods inaccordance with the present disclosure, it may be helpful to initiallydiscuss how light travels through a wafer, even when the wafer containsfront side or back side coatings and how the intensity of light changesbased upon its travel path.

For example, referring to FIG. 18, a substrate or wafer 14 is shownincluding a front side coating 80 and a back side coating 82. A ray ofincident power 84 is shown contacting the front side coating 80 of thewafer 14.

A general wafer 14 as shown in FIG. 18 has various properties thatshould be considered when practicing methods according to the presentdisclosure. For instance, the two surfaces of the wafer may havedifferent reflectivities and transmissivities. Furthermore, thereflectivities of the surfaces may be different for radiation incidenton them from outside the wafer, or from within the wafer. The surfaceregions may include various films and patterns that affect thesereflectivities and transmissivities. These surface regions (on bothfront and back of the wafer) cover the substrate material that forms thebulk of the wafer. When a wafer is semi-transparent, multiplereflections of the various beams of energy propagating within the waferaffect its front side reflectance, R*_(WF), and its transmittance, S*,as observed from outside the wafer. All of the optical properties may befunctions of wavelength, λ, and of temperature, T.

In the discussion below, T_(t) is the transmissivity of the top surfaceof the wafer, T_(b) is the transmissivity of the bottom surface of thewafer, R_(tv) is the reflectivity of the top surface of the wafer forradiation incident on it from outside the substrate, R_(ts) is thereflectivity of the top surface of the wafer for radiation incident onit from within the substrate and R_(bs) is the reflectivity of thebottom surface of the wafer for radiation incident on it from within thesubstrate. In general, if the incident radiation is not at normalincidence, all of the properties will be functions of the angle ofincidence and the plane of polarization of the radiation.

In general, the material of the bulk of the wafer has an absorptioncoefficient, α(λ,T) that is a function of the wavelength of theradiation, λ, and the temperature T. The attenuation in intensityexperienced by a ray passing through the substrate, can be described bythe quantitya=exp(−α(λ,T)d/cos θ_(i)),  (1)where d is the thickness of the substrate and θ_(i) is the internalangle of propagation. The latter angle is the angle between thedirection of the ray and the normal to the wafer surface. As usedherein, the quantity “a” refers to the internal transmittance.

In FIG. 19, we see that the intensity of the reflected ray R1 is onlyaffected by the reflectivity of the front surface of the wafer (WF),R_(tv), so that if the incident ray has intensity I, then ray R1 hasintensity R_(tv)I. The ray that has been transmitted into the substratehas intensity T_(t)I just at the point where it has passed through thefront surface region into the bulk of the wafer. As the ray A1 traversesthe substrate it loses intensity because of absorption of energy. As aresult it has an intensity aT_(t)I just at the point where it reachesthe back surface region (WB). The portion that is reflected at the backsurface to form the internal ray A2 has intensity aT_(t)R_(bs)I, and theportion that is transmitted to form the ray T1 has intensityaT_(t)T_(bs)I. When the reflected ray A2 reaches the front surface ithas lost more intensity as a result of absorption in the substrate andnow has intensity a²T_(t)R_(bs)I. The portion of ray A2 that isreflected at the front surface to form ray A3 initially has intensitya²T_(t)R_(bs)R_(ts)I, whereas the portion that is transmitted back outthrough the front surface forms ray R2, having an intensity a²T_(t)²R_(bs)I. When ray A3 reaches the back surface it has an intensitya³T_(t)R_(bs)R_(ts)I. The portion of A3 that is reflected, forming rayA4, initially has intensity a³T_(t)R_(bs) ²R_(ts)I, whereas the portionthat is transmitted through the back surface, forming ray T2, hasintensity a³T_(t)R_(bs)R_(ts)T_(b)I. When ray A4 reaches the frontsurface it has intensity a⁴T_(t)R_(bs) ²R_(ts)I. The portion reflectedfrom front surface to form ray A5 has an intensity a⁴T_(t)R_(bs) ²R_(ts)²I, whereas the portion that is transmitted through the front surface toform ray R3 has an intensity a⁴T_(t) ²R_(bs) ²R_(ts)I. From this pointon, it is easy to see that as more multiple reflections occur, each ofthe successive transmitted or reflected rays that emerge from thesubstrate will be further attenuated relative to the previous one. Theattenuation arises as a result of two passages through the substrate andby a reflection from the top surface and from the bottom surface, sothat each ray decreases in intensity by a factor of a²R_(ts)R_(bs),relative to the previous ray.

The total intensity transmitted by the wafer can be obtained by summingup all the components T1, T2, etc. which make up a sequence of the formaT_(t)T_(b)I+aT_(t)T_(b)(a²R_(ts)R_(bs))I+aT_(t)T_(b)(a²R_(ts)R_(bs))²I+aT_(t)T_(b)(a²R_(ts)R_(bs))³I+. . . ,  (2)which can be simplified to the expressionIaT_(t)T_(b){1+a²R_(ts)R_(bs)+(a²R_(ts)R_(bs))²+(a²R_(ts)R_(bs))³+ . . .}.  (3)Likewise the total intensity reflected from the wafer can be obtained bysumming all the components R1, R2, R3, etc. which make up a sequence ofthe formR_(tv)I+a²T_(t) ²R_(bs)I+a²T_(t) ²R_(bs)(a²R_(ts)R_(bs))I+a²T_(t)²R_(bs)(a²R_(ts)R_(bs))²I+a²T_(t) ²R_(bs)(a²R_(ts)R_(bs))³I+ . . .,  (4)which can be simplified to the expressionI└R_(tv)+a²T_(t)²R_(bs){1+a²R_(ts)R_(bs)+(a²R_(ts)R_(bs))²+(a²R_(ts)R_(bs))³+ . . .}┘.  (5)The expressions (3) and (5) include geometric series which can bereduced to simpler expressions. Taking the ratio of the totaltransmitted energy to the incident intensity, I, gives the transmittanceof the wafer as $\begin{matrix}{S^{*} = {\frac{{aT}_{t}T_{b}}{1 - {a^{2}R_{ts}R_{bs}}}.}} & (6)\end{matrix}$Likewise, the reflectance for the front side of the wafer is given bythe expression $\begin{matrix}{R_{WF}^{*} = {R_{tv} + {\frac{a^{2}T_{t}^{2}R_{bs}}{1 - {a^{2}R_{ts}R_{bs}}}.}}} & (7)\end{matrix}$

In general, the transmittance and the reflectance also depend on theangle of incidence and the plane of polarization being considered. Thisissue can be handled by considering the two orthogonal planes ofpolarization, the p- and s-polarization states, separately. For eachcase, the appropriate reflectivities and transmissivities are used todetermine the corresponding reflectance and transmittance. Theemittance, ε_(WF) or absorptance, A_(WF) of the front side of wafer forany given wavelength, angle of incidence and polarization state can beobtained from the expressionε_(WF) =A _(WF)=1−S*−R* _(WF).  (8)Combining equations 6, 7 and 8 we can deduce that $\begin{matrix}{ɛ_{WF} = {A_{WF} = {1 - R_{tv} - {\frac{{aT}_{t}\left( {T_{b} + {{aT}_{t}R_{bs}}} \right)}{1 - {a^{2}R_{ts}R_{bs}}}.}}}} & (9)\end{matrix}$

This expression can be used to calculate the emittance or absorptance ofthe front side of the wafer, given the appropriate set of data on thereflectivities, transmissivities of the surfaces as well as theabsorption coefficient and thickness of the substrate.

Determination of Specific Properties by Selectively Collecting Energyfrom Specific Rays

Conventional measurements do not discriminate between the various raysof reflected or transmitted light that contribute to the total intensitytransmitted or reflected by the wafer. As a result, information is lostthat may be useful in characterizing the wafer properties. For example,by selectively measuring the intensity of ray R1, the quantity R_(tv)can be deduced directly, without needing to know a, T_(t), R_(bs) orR_(ts), as would be required if R*_(WF) was measured. Likewise, byselectively measuring the intensity of ray T1, the quantity aT_(t)T_(b)can be determined, without needing to know R_(bs) or R_(ts), as would berequired if S* were measured.

Furthermore, by selectively measuring the intensity of other rays, onecan obtain even more information. For example, if the internaltransmittance, a, is determined then equation 1 can be used to deducethe absorption coefficient. The absorption coefficient can be calculatedby rearranging equation 1 to give $\begin{matrix}{{{\alpha\left( {\lambda,T} \right)} = {{- \frac{\cos\quad\theta_{i}}{d}}\ln\quad a}},} & (10)\end{matrix}$and for normal incidence this simplifies to the case where θ_(i)=0, sothat $\begin{matrix}{{\alpha\left( {\lambda,T} \right)} = {- {\frac{\ln\quad a}{d}.}}} & (11)\end{matrix}$

In cases where the radiation is not incident at normal incidence, theangle θ_(i) can be obtained from Snell's law. In practice the refractiveindex of most semiconductor materials is rather high (>3), so that anapproximation that θ_(i)≅0 usually results in less than 7% error in thevalue obtained for the absorption coefficient, and if the angle ofincidence of the radiation impinging on the wafer is <30°, then theerror would typically be less than 2%.

By selectively measuring the intensity of ray R2, the quantity a²T_(t)²R_(bs) can be obtained. This is especially useful because itsdependence on the internal transmittance enables us to use a measurementof a component of reflected light to deduce the magnitude of opticalabsorption in the substrate. Although optical absorption in thesubstrate is usually determined by performing transmittancemeasurements, in some circumstances it may be difficult to perform atransmittance measurement, because of geometric, mechanical or otherconstraints, in which case it would be useful to use a reflectionmeasurement to achieve this goal. Although R*_(WF) is also affected bythe internal transmittance, it may be difficult to use a direct ofmeasurement of R*_(WF) to deduce the internal transmittance. Forexample, if the intensity of ray R1 is much larger than that of ray R2then a measurement of R*_(WF) is dominated by the first surfacereflection, R_(tv), which does not depend on the internal transmittance.As a result it may be difficult to make a very accurate determination ofthe contribution of rays R2, R3, etc. to the reflectance. This makes thedetermination of the internal transmittance based on a measurement ofR*_(WF) more prone to error. In contrast, the intensity of ray R2 isdirectly affected by the magnitude of the internal transmittance, so itsmeasurement can give a more accurate estimate.

The reflected component R2 is also influenced by the transmissivity ofthe top surface of the wafer, T_(t), and by the reflectivity of the backsurface, R_(bs). Hence by measuring the intensity of R2, the aboveproperties may also be determined. The reflectance, R*_(WF) is alsosensitive to them, as a result of the contributions of ray R2, R3, etc.However, it is also affected by R_(tv) and R_(ts), so it may be moredifficult to use a measurement of R*_(WF) to deduce T_(t) or R_(bs).

Selective measurements of individual contributions of any of the otherrays may also be useful in various circumstances. For example the ray T2is sensitive to the quantities a, T_(t), T_(b), R_(bs) and R_(ts). Ameasurement of the intensity of this ray allows a transmissionmeasurement to provide information about the reflectivity of the frontsurface for radiation incident from within the substrate, R_(ts). Theratio of intensities of rays can also be useful. For example, the ratioof the intensity of rays T2 to T1, or R3 to R2 gives the quantitya²R_(ts)R_(bs).

Separate Measurements of Back Surface of Wafer and Front Surface

For fuller characterization of the properties of the wafer, it may beuseful to arrange for separate measurements of reflected and/ortransmitted light components to be made for light incident on the waferfrom two opposite sides. For example the ray of light A0 may be incidenton the side marked WF as shown in FIG. 19 or it could be incident on theside WB.

If ray A0 is incident at the same angle and with the same polarization,the transmitted light components T1, T2 etc should be the same for bothschemes. This is evident when one inspects the terms in the series inexpression 2, because each term (each of which corresponds to theintensity of a transmitted ray) is unchanged if one exchanges thesubscript t for the subscript b. The exchange of subscripts is themathematical equivalent of changing the surface that is illuminated fromWF to WB. The consistency of transmitted light measurements for the twoillumination conditions can be used to check that the measurementapparatus is functioning properly. However, if either of the wafersurfaces has any features that cause scattering of light, then thepattern of reflected or transmitted rays may be more complex, and theintensity measurements may become sensitive to the side that isilluminated. This may also be true if the bulk of the wafer can scatterlight.

Although the transmitted ray components should be equivalent regardlessof which surface is illuminated, the same is not true for the reflectedlight components. As a result, illumination of the surface WB, providesnew information about the optical properties of the wafer. Thereflectance of the wafer, when the wafer is illuminated on the frontside, R*_(WF) is not necessarily equal to that when the back side isilluminated, R*_(WB). R*_(WF) is given by the equation 7 but R*_(WB) isgiven by the equation $\begin{matrix}{{R_{WB}^{*} = {R_{bv} + \frac{a^{2}T_{b}^{2}R_{ts}}{1 - {a^{2}R_{ts}R_{bs}}}}},} & (12)\end{matrix}$where R_(bv) is the back surface reflectivity for radiation incident onit from outside the wafer.

Likewise, the various reflected light rays for front-side illumination,which we may designate as R1 _(WF), R2 _(WF), R3 _(WF), etc. do notnecessarily match the corresponding rays for back-side illumination,designated as R1 _(WB), R2 _(WB), R3 _(WB), etc. The origins of thisasymmetry become evident when one inspects the terms in the series ofexpression 4, because each term (each of which corresponds to theintensity of a reflected ray) is changed if one exchanges the subscriptt for the subscript b. This asymmetry allows a measurement withback-side illumination to provide extra information about the opticalproperties of the wafer. In particular, we see that the first reflectedray R1 _(WB), can provide a measurement of the back surface reflectivityfor radiation incident from outside the wafer, R_(bv). Furthermore,measurement of the intensity of the second reflected ray, R2 _(WB), canprovide a measurement of the quantity a²T_(b) ²R_(ts).

From this discussion it is clear that measurements of reflected and/ortransmitted light components for the case of illumination from the frontand back sides of the wafer can provide many useful pieces ofinformation about the optical properties of the wafer. It should also benoted that it is also possible to extract information about the opticalproperties from measurements of the absorptance or the emittance ofeither or both surfaces of the wafer. These quantities are alsogenerally not equal for the two sides of the wafer. The emittance of thefront side of the wafer, ε_(WF), and its absorptance, A_(WF), can bededuced from equation 8, which leads to equation 9, whereas theemittance of the back side of the wafer, ε_(WB), and its absorptance,A_(WB), are given byε_(WB) =A _(WB)=1−S*−R* _(WB),  (13)which leads to the equation $\begin{matrix}{ɛ_{WB} = {A_{WB} = {1 - R_{bv} - {\frac{{aT}_{b}\left( {T_{t} + {{aT}_{b}R_{ts}}} \right)}{1 - {a^{2}R_{ts}R_{bs}}}.}}}} & (14)\end{matrix}$

Although the direct measurement of these quantities requires specialinstrumentation, it is possible. For example, the emittance at any givenwavelength can be deduced by measuring radiation that is thermallyemitted by the wafer. By comparing the strength of the thermal emissionfrom the wafer to that from a black-body radiator at a temperature equalto that of the wafer, it is possible to deduce the emittance. Suchmeasurements can be used to measure ε_(WF) and ε_(WB). The absorptanceat a given wavelength can be measured by illuminating the wafer with aknown intensity of radiation at that wavelength and observing how thetemperature of the wafer changes over time. The increase in wafertemperature can be related to the absorptance of the wafer at thewavelength of interest. Such measurements can be used to determineA_(WF) and A_(WB).

Acquiring Information About Wafer Properties from Measurements

The measurements described in this disclosure can be used for variouspurposes, including characterization of the type of wafer beingprocessed. For example, the optimal processing approach might requireinformation about the substrate material, its doping, the waferthickness and the reflectances and transmittances of the wafer for givenranges of wavelengths. Such information can then be used to predict thetemperature dependence of the spectral emittance or absorptance, or thetotal emittance or absorptance. That information can then be used toimprove the uniformity and repeatability of thermal processing and canalso be used to optimize the control of the heating process for greatesttime efficiency and hence best wafer throughput. Although informationabout the type of wafer being processed can be separately provided tothe processing equipment, sometimes this is not convenient or theinformation is not available. In this case, an in situ determination ofthe desired properties, either immediately before processing or evenduring an early part of the processing, may be desirable.

For example, by obtaining an estimate of the internal transmittance,which is linked to the absorption coefficient α(λ,T), one can find outabout the type of wafer being processed, because the material propertiesof the substrate affect its absorption spectrum, which is described bythe wavelength dependence of α(λ,T). In principle, the type of waferbeing processed can be identified through a measurement of itsabsorption spectrum. For example, the material that the substrate ismade from can be identified by comparing the measured absorptionspectrum to a set of absorption spectrum data for various materials. Forexample, if the wafer being processed was lightly-doped silicon, with aresistivity greater than 1 Ωcm, the absorption spectrum displays a largedecrease in absorption as the wavelength increases from 0.8 μm, whereα(λ,T) at room temperature is ˜850 cm⁻¹, to 1.2 μm, where α(λ,T) at roomtemperature is ˜0.02 cm⁻¹. This sharp feature is often called theabsorption edge, and its spectral location is linked to the magnitude ofthe minimum energy gap in the band structure of the material.Identification of such a characteristic feature in the absorptionspectrum can help identify the wafer substrate as being made of silicon.

In contrast, if the wafer were made from germanium, the absorption edgefeature would appear in the wavelength range near 1.8 μm. A similarapproach can be used to distinguish the presence of other materials,such as GaAs, InP, InSb, GaSb, GaN, InN, SiC and diamond, because theabsorption spectra of these materials also show an absorption edge. Itcan also be used to identify the presence of alloys of semiconductors,such as silicon-germanium alloys, or quaternary alloys of GaAs and InP.Analysis of the absorption spectra can even be used to deduce thecomposition of these alloys, such as the ratio of the Si to Ge content.In principle analysis of α(λ,T) can also be used to distinguish betweenvarious types of insulators and metals, as well as for semiconductors,because most materials display characteristic features in theirabsorption spectra.

For example, many materials display absorption features that arises as aconsequence of transitions of electrons between energy levels. Suchfeatures typically arise at wavelengths in the ultra-violet (UV),visible and near-infra-red parts of the electromagnetic spectrum. Manymaterials also display absorption features linked to vibration of atomicspecies about their mean positions. Such features typically arise atinfra-red wavelengths. A comparison of a measured absorption spectrumwith reference information about the spectral positions of absorptionedges, electronic transitions and vibrational absorption features can beused to identify the material being processed. It is important torealize that absorption phenomena can affect reflected light intensityas well as transmitted light intensity, and measurement of either can beused to deduce information about the absorption spectrum. Furthermore,in the case of opaque surfaces, analysis of the reflection spectrum canalso provide similar information.

The absorption spectrum can also be used to determine the state ofdoping of the wafer. For example, the presence of electrically activedopants results in the phenomenon of free-carrier absorption. Thefree-carrier absorption results from interaction of electromagneticradiation with charge carriers that can move through the semiconductorlattice. The strength of the absorption depends on the concentration offree carriers. In semiconductors the free carriers can be electrons orholes, depending on the nature of the doping. In an n-typesemiconductor, the dominant charge carriers are electrons, whereas in ap-type semiconductor the dominant charge carriers are holes. Thewavelength and temperature dependence of free-carrier absorption can beestimated from theoretical or empirical models. Such models can alsoinclude other effects of doping on the absorption spectrum, such as theband-gap narrowing in heavily doped semiconductors, and absorptionassociated with transitions between bands. By collecting informationabout the absorption spectrum and analyzing the spectrum with a model,it is possible to determine the type of the carriers (electrons orholes) and their concentration. This information can then be used topredict the behavior during the semiconductor manufacturing step.

As well as providing information about the substrate, the measurementsof optical properties can provide information about surface coatings andpatterns on the wafer. The wafer may be coated on both the front and theback side. These coatings may be made up of a stack of several films.They may also be laterally patterned to form various device features,and there may also be trench-like features and other non-planarstructures present. Typically the device features would be on the frontside of the wafer, previously referred to as WF. The opticalmeasurements described in this disclosure may also help characterize thenature of the features and layers present near the surfaces of thewafer. The information gained from that characterization can then beused to improve process control during the semiconductor manufacturingstep. Here, the ability to discriminate between front and back surfacereflections can be useful in forming a more complete understanding ofthe nature of the films and structures on either surface of the wafer.Both reflected light and transmitted light measurements can be affectedby the optical properties of the two surfaces of the wafer, as will bediscussed further below.

Comparison of the various reflected and transmitted light measurementscan help to identify whether at any given wavelength the films on eithersurface are transparent or opaque, and whether the substrate istransparent or opaque. For example, if the films on the wafer surfaceare opaque, i.e. T_(t)=0, as may be the case if the wafer is coated witha metal layer, then the front surface reflectance R*_(WF)=R1 _(WF) andthe higher order reflections, R2 _(WF), R3 _(WF) etc are all zero. Inthis case both the transmittance, S*, and all the transmitted lightcomponents T1, T2 etc. are also zero. However, if the substrate is notopaque, i.e. a≠0, and the back surface layers are not opaque, i.e.T_(b)≠0, then the back surface reflectance R*_(WB)≠R1 _(WB) and R1_(WB)≠0. Hence a comparison of reflected light components for front andback surface illumination can help identify whether the films on one ofthe surfaces of the wafer are opaque. If we find that for one surfacethe reflectance is the same as the surface reflectivity, whereas for theother surface this does not hold, then it is likely that the formersurface includes an opaque film. One should note that if the backsurface reflectivity R_(BS)=0, then the front surface reflectance wouldalso equal its reflectivity because there would be no secondaryreflections, but in this case the transmittance would not be zero,unless the front surface happened to be a perfect reflector. Suchcircumstances are unlikely to arise in practice. The approach can beequally well applied to finding opaque films on the front or backsurfaces of the wafer. Other measured quantities can be analyzed withthe same purpose. For example, if the transmittance, S* or the firsttransmitted light component, T1, is zero, and yet the back surfacereflectance R*_(WB)≠R1 _(WB) and R1 _(WB)≠0, then we can deduce that thefront surface is opaque.

If the wafer substrate is opaque, then a=0 and the reflectance of eachsurface of the wafer is equal to its reflectivity, i.e. R*_(WF)=R_(tv)and R*_(WB)=R_(bv). Furthermore the reflected light components R2 _(WF),R3 _(WF), etc. and R2 _(WB), R3 _(WB) etc. are zero. Furthermore, thetransmittance, S*=0, and all the transmitted light components T1, T2,etc are also all zero. Hence an analysis of these components ofreflected or transmitted energy can be used to deduce whether thesubstrate material is opaque at any given wavelength. However, we shouldnote that the same conditions (i.e. R*_(WF)=R_(tv), R*_(WB)=R_(bv),S*=0, T1=0, T2=0 etc.) may arise if the films on both surfaces areopaque, i.e. if both T_(t)=0 and T_(b)=0, even if the substrate itselfis transparent, i.e. a≠0.

Another test that can be applied to determine whether a surface of thewafer contains an absorbing film is to test whether its reflectivity isthe same for radiation incident from within the substrate as forradiation incident from outside the substrate, e.g. if R_(tv)≠R_(ts),then the top surface of the wafer contains an absorbing film.Furthermore if R_(tv)≠(1−T_(t)) then the top surface contains anabsorbing film. Analogous rules can be applied to characterize the backsurface of the wafer.

If the top and bottom films are all transparent and the wafer is alsotransparent, then a special case arises, where the reflectance is equalfor light incident from either side of the wafer. In this case$\begin{matrix}{R_{WF}^{*} = {R_{WB}^{*} = {\frac{R_{tv} + R_{bv} - {2R_{tv}R_{bv}}}{1 - {R_{tv}R_{bv}}}.}}} & (15)\end{matrix}$As a result, a simple test of whether a wafer and all its coatings arenon-absorbing is to check if R*_(WF)=R*_(WB).

By selecting the wavelength range where such diagnostic tests areperformed, different aspects of the wafer's characteristics can beprobed. For example, by choosing a wavelength range in the infra-redregion such as 1.55 μm, if it is detected that the wafer shows anappreciable absorption coefficient, e.g. greater than 1 cm⁻¹, then thewafer must be heavily doped, e.g. with a resistivity below 0.1 Ωcm. Theexact criterion for definition of the appropriate absorption leveldepends on the wavelength, in a manner that can be determined from themodel for the effect of doping on optical absorption. For any test it isbetter to perform the measurement at several wavelengths, in order toreduce the possibility that an unusual combination of surfacereflectivities or some other condition produces a false result. Thetests can also be performed using a broadband light source that deliverslight over a range of wavelengths if desired.

Determination of Absorption Coefficient of the Substrate

In order to deduce the value of α(λ,T), it is usually necessary todeduce the internal transmittance given by equation 1. The internaltransmittance may be obtained by measurement of any of the reflected ortransmitted light components illustrated in FIG. 19, or from analogouscomponents obtained from measurements where the surface WB isilluminated. However, in general it is also necessary to know otherproperties of the wafer. For example, by rearranging expression 7, “a”is given by the expression $\begin{matrix}{a = {\sqrt{\frac{R_{WF}^{*} - R_{tv}}{\left\{ {{\left( {R_{WF}^{*} - R_{tv}} \right)R_{ts}} + T_{t}^{2}} \right\} R_{bs}}}.}} & (16)\end{matrix}$Hence, in order to obtain a value for a, R*_(WF), R_(tv), R_(ts), T_(t)and R_(bs) should be known. Although these quantities may be known fromother measurements or calculations, in general they are unknown. Themethod described in this disclosure can help to improve the estimate ofa, because a value for the first surface reflection R_(tv) can beestablished, by measuring the reflected light component R1. Thereflectance R*_(WF) can also be established by conventional means. Inmany cases of practical importance the methods of this disclosure canfurther provide complete characterization of the optical properties ofinterest, including an accurate determination of the internaltransmittance, and hence of the absorption coefficient α(λ,T).

The internal transmittance can also be obtained from transmitted lightmeasurements. Rearranging the expression 6, the expression following isobtained: $\begin{matrix}{a = {\frac{{{- T_{t}}T_{b}} + \sqrt{{T_{t}^{2}T_{b}^{2}} + {4R_{ts}{R_{bs}\left( S^{*} \right)}^{2}}}}{2R_{ts}R_{bs}S^{*}}.}} & (17)\end{matrix}$Here, in order to obtain a value for a, S*, T_(t), R_(ts), T_(b) andR_(bs) need to be known. Once again, these quantities may be known fromother measurements or calculations, but in general they are unknown.Values for the internal transmittance can also be derived frommeasurements of specific components of the reflected or transmittedradiation. For example, as shown above, the ray T1 has intensity I_(T1),given by aT_(t)T_(b)I. Hence, the internal transmittance is deduced fromthe expression $\begin{matrix}{a = {\frac{I_{T\quad 1}}{T_{t}T_{b}I}.}} & (18)\end{matrix}$The internal transmittance can be obtained from a measurement of theintensity of the ray R2, I_(R2), which has an intensity a²T_(t)²R_(bs)I. Hence, the internal transmittance can be deduced from theexpression $\begin{matrix}{a = {\sqrt{\frac{I_{R\quad 2}}{T_{t}^{2}R_{bs}I}}.}} & (19)\end{matrix}$The internal transmittance can also be obtained from a measurement ofthe ratio of the intensities of successive reflected or transmittedrays, because each of the successive transmitted or reflected rays thatemerge from the substrate will be further attenuated relative to theprevious one. The attenuation arises as a result of two passages throughthe substrate and as a result of a reflection from the top surface andfrom the bottom surface, so that each ray decreases in intensity by afactor of a²R_(ts)R_(bs), relative to the previous ray. Hence if theintensity of ray R3 is I_(R3), then the ratio of I_(R3) to I_(R2), K, isgiven by K=I_(R3)/I_(R2)=a²R_(ts)R_(bs), and we can deduce a from$\begin{matrix}{a = {\sqrt{\frac{K}{R_{ts}R_{bs}}}.}} & (20)\end{matrix}$A similar approach can be used for the ratio of successive transmittedrays, such as T1 and T2 etc.The Case where Surface Coatings do not Absorb Radiation

The case where neither the top nor bottom surface of the wafer containsabsorbing films is of special interest. In this situationT_(t)=1−R_(tv), T_(b)=1−R_(bv), R_(tv)=R_(ts) and R_(bv)=R_(bs). Thisallows us to rearrange the expressions for reflectances andtransmittance in terms of quantities that we can measure using themethods described in this disclosure, including the first surfacereflectivities, R_(tv) and R_(bv), which can be obtained from R1 _(WF)and R1 _(WB) respectively. The expressions are $\begin{matrix}{R_{WF}^{*} = {R_{tv} + {\frac{{a^{2}\left( {1 - R_{tv}} \right)}^{2}R_{bv}}{1 - {a^{2}R_{tv}R_{bv}}}.}}} & (21)\end{matrix}$Likewise, the reflectance of the wafer for light incident from the backside is given by $\begin{matrix}{R_{WB}^{*} = {R_{bv} + {\frac{{a^{2}\left( {1 - R_{bv}} \right)}^{2}R_{tv}}{1 - {a^{2}R_{tv}R_{bv}}}.}}} & (22)\end{matrix}$The transmittance is given by $\begin{matrix}{S^{*} = {\frac{{a\left( {1 - R_{tv}} \right)}\left( {1 - R_{bv}} \right)}{1 - {a^{2}R_{tv}R_{bv}}}.}} & (23)\end{matrix}$Any of these expressions 21, 22 or 23 can be used to deduce the internaltransmittance, and hence to determine the absorption coefficient of thesubstrate α(λ,T), from the measured quantities. For example, rearranging21, the following expression is obtained $\begin{matrix}{a = {\sqrt{\frac{R_{WF}^{*} - R_{tv}}{\left\{ {{\left( {R_{WF}^{*} - R_{tv}} \right)R_{tv}} + \left( {1 - R_{tv}} \right)^{2}} \right\} R_{bv}}}.}} & (24)\end{matrix}$The method described in this disclosure can be used to deduce all thequantities in the expression on the right hand side of equation 24, andhence can be used to make an accurate determination of the internaltransmittance. The reflectance, R*_(WF), can be obtained by conventionalmeans, and the reflectivity R_(tv) and the reflectivity R_(bv) can bedetermined by the method described in this disclosure. For example, byilluminating the front surface of the wafer and collecting only thelight reflected one time at the front surface of the wafer, thereflectivity R_(tv) can be deduced. Then, by illuminating the backsurface of the wafer and collecting only the light reflected one time atthe back surface of the wafer, the reflectivity R_(bv) can be deduced.Having measured R*_(WF), R_(tv) and R_(bv), the internal transmittancefrom equation 24 can be calculated. The internal transmittance can alsobe deduced from an analogous approach where the back surface reflectanceR*_(WB), is measured in combination with the use of equation 22.Furthermore, the internal transmittance can be deduced from ameasurement of the transmittance S*. In the latter case, the internaltransmittance is obtained from the expression $\begin{matrix}{{a = \frac{\begin{matrix}{{{- \left( {1 - R_{tv}} \right)}\left( {1 - \quad R_{bv}} \right)} +} \\\sqrt{{\left( {1 - R_{tv}} \right)^{2}\left( {1 - R_{bv}} \right)^{2}} + {4R_{tv}{R_{bv}\left( S^{*} \right)}^{2}}}\end{matrix}\quad}{2R_{tv}R_{bv}S^{*}}},} & (25)\end{matrix}$obtained by rearranging equation 23. Once again, once the transmittanceS* is obtained, and the reflectivities R_(tv) and R_(bv) are obtained,equation 25 can be used to deduce the internal transmittance. Likewise,the internal transmittance can be obtained from measurements of thetransmitted ray, T1 and using the expression $\begin{matrix}{{a = \frac{I_{T\quad 1}}{\left( {1 - R_{tv}} \right)\left( {1 - R_{bv}} \right)I}},} & (26)\end{matrix}$obtained by rearranging equation 18. The internal transmittance can alsobe obtained by measuring the intensity of the reflected ray, R2 andusing the expression $\begin{matrix}{a = \sqrt{\frac{I_{R\quad 2}}{\left( {1 - R_{tv}} \right)^{2}R_{bv}I},}} & (27)\end{matrix}$obtained by rearranging equation 19. The internal transmittance can beobtained by measuring the ratio of the intensities of successivereflected or transmitted rays and using the expression $\begin{matrix}{{a = \sqrt{\frac{K}{R_{tv}R_{bv}}}},} & (28)\end{matrix}$obtained by rearranging equation 20.

In summary, for the case where the films on both the front and the backof the wafer are non-absorbing, the method of this disclosure allows anaccurate determination of the absorption coefficient of the substratematerial. In cases where the films are absorbing, further measurementsor modeling may be needed to reach a sufficiently accurate determinationof the absorption coefficient. However, the case where surface films arenon-absorbing is of practical importance, because this condition arisesin important practical applications, such as oxidation or depositionprocesses performed early on in the device fabrication sequence, andalso in some annealing processes on semiconductor wafers, such as ionimplantation damage annealing. In such processes, the surface films arefrequently relatively transparent, at least for wavelengths in theinfra-red. Furthermore, in many cases where there are patterned filmspresent on the wafer and even if these films themselves are absorbing,the patterning means that the absorbing film only partly cover thesurface of the wafer and hence it allows the transmission of asignificant fraction of the incident radiation into the substrate. Itshould be understood that the analysis for the case of non-absorbingfilms may still be reasonably accurate even if the surface films do showsome absorption, provided that the internal transmittance, a, is rathersmall, as compared to the transmissivity of either the front or backsurface of the wafer, T_(t) and T_(b). The success of the approach candepend on the strength of the absorption in any surface layers and/orthe degree of surface coverage. Hence the approach may even be used insituations where there are absorbing films present, such as metals,silicides or heavily doped semiconductor regions, provided that thedegree of absorption introduced by these features is small relative tothat introduced by the propagation of radiation through the substrate tothe opposite surface. Typically wafers do not have thick layers ofabsorbing material present on their back surfaces, so that it is oftenreasonable to assume that the back surface is non-absorbing.

FIG. 20 shows an example of the temperature dependence of some opticalproperties of a slab of material at a wavelength λ. In the example, theabsorption coefficient of the material that makes up the bulk portion ofthe slab (usually referred to as the substrate), α(λ,T) varies withtemperature. As a result, the internal transmittance, also changes withtemperature. In the following discussion, the methods of this disclosureare further described in detail to show how they can be used to predictoptical properties as a function of temperature. The approach usedrelies on the combination of low temperature measurements of the surfacereflectivities with a model for the optical absorption of silicon.

In the example shown, the case considered is that for a silicon waferthat is lightly doped. In this instance, lightly doped means that theresistivity is greater than −1 Ωcm. The wafer considered has a thicknessof 775 μm, which is typical for a 300 mm diameter silicon wafer as usedin semiconductor device manufacturing. In this example, the reflectivityof the front surface of the wafer is R_(tv)=0.3, and the reflectivity ofthe back surface of the wafer is R_(bv)=0.6, and it is assumed that thereflectivities of these two surfaces do not change with temperature andthat there are no absorbing films present at the surfaces. The opticalproperties are calculated as functions of temperature, for a wavelengthof 2.3 μm. In this example, the calculation is performed for radiationincident on the wafer at normal incidence or emitted from the wafer atnormal incidence. The quantities calculated were the reflectance of thefront of the wafer, R*_(WF), and the back of the wafer, R*_(WB), thetransmittance of the wafer, S*, and the emittance of the front of thewafer, ε_(WF), and of the back of the wafer, ε_(WB). These quantitieswere obtained from the combination of equations 6, 7, 9, 12 and 14above. All these quantities are functions of wavelength and temperature,and in this example, the temperature dependence arises because theinternal transmittance is a function of temperature. The temperaturedependence of internal transmittance arises because of the temperaturedependence of the absorption coefficient, α(λ,T). For the calculationsshown here α(λ,T) for the wavelength of 2.3 μm was obtained from themodel given by Vandenabeele and Maex in J. Appl. Phys. 72, 5867 (1992).In general, the model used to deduce α(λ,T) can be any theoretical orempirical model for the wavelength and temperature dependence of theabsorption coefficient of the material of interest. For example, forlightly doped silicon, the model for optical absorption described byRogne et al. in Appl. Phys. Lett. 69, 2190 (1996) provides a way tocalculate α(λ,T) for wavelengths between ˜1 and ˜9 μm, for temperaturesbetween room temperature and ˜800° C. Timans provides data and modelsfor optical absorption and refractive indices of both lightly andheavily doped silicon in the chapter “The Thermal Radiative Propertiesof Semiconductors” in the book “Advances in Rapid Thermal and IntegratedProcessing”, edited by F. Roozeboom (Kluwer Academic Publishers,Dordrecht, Netherlands, 1995) p. 35. Such models can provide estimatesfor a wide range of wavelengths, from the visible region where λ˜0.5 μmthrough to the far infrared, where λ˜30 μm. The models described canalso take account of the substrate doping conditions, such as the dopingconcentration, or other information about the concentrations ofelectrons and holes in the substrate. Other suitable models have beendescribed in the literature, including models such as the Drude modelfor free-carrier absorption, which can be used to estimate the effect ofelectron and hole concentrations on infra-red absorption.

The other information that is needed for the predictions of optical andthermal properties is the thickness of the wafer. Depending on theaccuracy needed in the prediction, the thickness can either be estimatedas an appropriate thickness for the wafer size being processed, it canbe provided as an input parameter by the user, or it can be measuredeither manually or automatically within the tool.

In the example shown, α(λ,T) at 2.3 μm is very low at low temperatures,for example it is estimated to be <10⁻⁶ cm⁻¹ at room temperature. Underthis condition, a≅1. In contrast, at high temperature, α(λ,T) is large,for example it is ˜100 cm⁻¹ at 730° C. In that case, a≅0.00054. As thetemperature rises further the internal transmittance tends towards zero,and the wafer becomes opaque. The figure shows how the internaltransmittance remains ˜1, and the substrate is effectively transparent,for temperatures below ˜250° C., but as the temperature rises theinternal transmittance decreases, until at temperatures >750° C., thewafer is effectively opaque. In the interval between 250 and 750° C.,the wafer can be said to be semi-transparent.

At low temperatures, where the wafer is transparent, the transmittanceS*=0.34, but this falls towards zero as the temperature rises, becoming<10⁻⁴ for temperatures >750° C. At low temperature, the reflectance forlight incident on the front surface equals the reflectance for lightincident on the back surface, as expected from equation 15 above. In theexample, at room temperature R*_(WF)=R*_(WB)=0.66. However, as thetemperature rises, both R*_(WF) and R*_(WB) decrease and they cease tobe equal. The decrease occurs because the increasing absorption withinthe substrate reduces the contribution of light reflected at the secondsurface (opposite the surface that is illuminated) to the reflectance.When the substrate becomes effectively opaque, then the reflectancesequal the corresponding reflectivities of the illuminated surfaces, sothat R*_(WF)=R_(tv)=0.3 and R*_(WB)=R_(bv)=0.6. The emittances of theslab as observed from the two opposite sides are both zero at lowtemperature, when the wafer is transparent. This is consistent with thefundamental principle that objects that cannot absorb radiation alsocannot emit radiation. As the temperature rises and the wafer becomessemitransparent, the emittances also increase, until at the point wherethe wafer is effectively opaque, they equal the correspondingemissivities of the surfaces, so that ε_(WF)=1−R_(tv)=0.7 andε_(WB)=1−R_(bv)=0.4.

This example shows how the present disclosure can provide estimates ofemittances, or the equivalent absorptances, at elevated temperatures. Inprinciple, these quantities can be deduced during heating, for exampleby making real-time measurements of R*_(WF) and S* within the processchamber and then calculating ε_(WF) from equation 8. However, in somecircumstances it can be difficult to perform an accurate measurementwithin the chamber. In contrast, the method of this disclosure allows adetermination of any of the properties of the wafer in a convenientlocation outside the process chamber. This can then be combined withknowledge of the trend of α(λ,T) with temperature, and knowledge of thethickness of the wafer to make a prediction of the emittance orabsorptance of the wafer during processing. In this example, ameasurement of R_(bv) at room temperature can be enough to ensure thedetermination of an appropriate value for ε_(WB) when the wafer is atT>750° C., inside the process chamber. The information on emittance canbe used to correct the readings of a pyrometer in order to determine thetemperature of the wafer. The modeling approach can also be used topredict the temperature dependence of the spectral absorptances of thewafer as functions of temperature. This information can be provided to acontrol algorithm in order to improve the control of the heatingprocess, for example by providing improved estimates of the powercoupling between the wafer and a lamp heating energy source, or byproviding an improved estimate of the radiated energy heat loss from thewafer.

The flow chart in FIG. 21 shows one embodiment of how to perform themethod of this disclosure. The first step is to load the wafer to aposition where an optical measurement can be performed. In the next stepthe optical properties are measured with the wafer at an initialtemperature, T1. The initial temperature may be near room temperature.The optical properties can be any of those mentioned in this disclosure.They can be measured using an approach that involves illuminating eithersurface of the wafer. The next step, which is optional, involvesdetermining the wafer's thickness. This determination can be through ameasurement or by collecting the information from an external input ofthat data. Various means of wafer thickness measurement could be usedhere, such as an optical, electrical or mechanical measurement. Usuallyit is best to perform the thickness measurement with a probe that doesnot touch the wafer surface, in order to prevent surface damage orcontamination, especially on the surface of the wafer where theelectronic devices are to be fabricated. For example, the thickness ofthe wafer can be measured by using an infrared interferometer. Thethickness can also be measured by using optical probes to make accuratesimultaneous measurements of the front and back surface positions andthen determining the distance between them. In this case the wafer neednot be transparent at the optical wavelengths employed by the probes.The optical probes can be based on methods of optical interferometry orthey could be based on methods of laser triangulation. The waferthickness can also be measured by electrical capacitance displacementprobes. It can also be measured by using air gauges that determinedimensions by sensing the impact of the location of surfaces on gas flowbehavior. It can also be determined by weighing the wafer, and usingestimates of the wafer's area and its density to deduce the thickness.In some cases, if the coatings on the wafer surfaces have a substantialthickness themselves, it may be necessary to take their thickness intoaccount when determining the thickness of the substrate itself. Thiscould be done by subtracting the thickness of the coatings from ameasurement of the thickness of the wafer that includes such coatings.

The next step, which is also optional, involves determining the wafer'sdoping. This determination can also be through a measurement or bycollecting the information from an external input of that data. If thedoping needs to be determined, typically this may require optical orelectrical measurement. As was pointed out above, the methods describedin this measurement may be used to help determine the nature of thesubstrate doping. The information on doping can include the type of thedoping, e.g. whether the wafer substrate is n-type or p-type material.It can also include the resistivity of the substrate. It can alsoinclude the species used to dope the substrate and the concentration ofthe dopant in the substrate. It can also include the concentration ofelectrons or holes in the substrate. Other methods of determining dopingcan include direct electrical measurements using contact or non-contactprobes. Non-contact probes would generally be preferred, in order toprevent surface damage or contamination. Non-contact probing methods caninclude sensing of eddy currents induced in the substrate by anoscillating electric or magnetic field applied to the wafer.

Other information can also be provided concerning the nature andproperties of the wafer. For example, information provided can includethe nature of the substrate of the wafer, such as whether the wafer issilicon, gallium arsenide, germanium etc. It can also includeinformation about the nature of films on the wafer, such as thethicknesses, materials and properties of thin films present on eithersurface of the wafer. It can also include information about the natureof patterns present on the wafer surfaces. Other properties that can beprovided can also include the thermal properties, such as the thermalconductivity, thermal diffusivity or specific heat capacity.Measurements of thickness and doping are described as being optionalbecause for some simple predictions of optical properties, it is notnecessary to know these quantities with a high degree of accuracy.However, a measurement of wafer thickness can also be useful for variouspurposes of improved process control. For example, the thermal mass ofthe wafer depends on its thickness. As a result, the heating or coolingrate of the wafer is affected by the wafer's thickness. A determinationof wafer thickness can help to improve the control of heating or coolingof the wafer. For example, the information about the wafer's thicknesscan be provided to a control algorithm that is used to set the heatingpower. This may also be helpful for controlling the process if theheating is open-loop i.e. without feedback control from a temperaturesensor monitoring the wafer's temperature. The information can be usedirrespective of the type of heating being employed, and can be employedwhen the wafer is heated by electromagnetic radiation, or by thermalconduction or by gas convection. For example it can be used to improvecontrol in a system where the wafer is heated by a hot-plate orsusceptor. By knowing the wafer thickness accurately it is easier topredict the evolution of wafer temperature after it is loaded onto ahot-plate. In this case, the improvements in control can be attainedeven without any measurements of optical properties of the wafer. Suchimprovements may be useful especially in cases where the wafer ispredominantly heated by thermal conduction. In that situation opticalproperties have less influence on heat transfer to and from the wafer,but the thermal mass of the wafer still has a strong effect on theheating cycle.

The next step is to use a model to predict the optical properties atleast at one second temperature of interest, T2. In practice this caninvolve predicting the optical properties over a range of temperatures,i.e. establishing the temperature dependence of the optical properties.The optical properties can again be any of those discussed in thisdisclosure, such as the emittance, absorptance, reflectance,transmittance or any of the surface reflectivities or emissivities etc.These properties can be predicted at any wavelength or temperature ofinterest.

The model used can be based on the equations given in this disclosure,or another set of equations or an algorithm that allows the predictionof the optical properties. The input to the model includes at least oneof the initial measurements performed at the first temperature, T1. Itmay also optionally include information on the wafer thickness and onthe doping of the wafer. In the case where the information on the dopingof the wafer is available, this can be used to predict how the opticalabsorption coefficient and/or the refractive index in the substratevaries with wavelength and/or temperature.

The next step involves using the information about the opticalproperties to estimate a parameter that is related to control of theheating process. Examples of parameters include the emittance of thewafer at a wavelength that is used by a pyrometer for sensing wafertemperature. In this case an improved estimate of the emittance canprovide a more accurate temperature reading. The pyrometer may ingeneral determine the wafer temperature based on a sensed value of theintensity of thermal radiation emitted by the wafer. The wafer emittanceor reflectance may be supplied to an algorithm that calculates the wafertemperature based on this sensed value of the intensity of radiationemitted by the substrate. Many schemes for pyrometry have been describedin the prior art. Approaches such as enhancing the emittance of thewafer by forming a reflective cavity confronting at least part of thewafer surface have been shown to help reduce the effects of emittancechanges on temperatures determined by pyrometers. However, improvedaccuracy is possible if an initial estimate of the emittance isavailable. Other approaches for reducing the effect of emittancevariation include methods where in situ optical measurements are used tomeasure the emittance of the wafer during processing. One such approachis the ripple pyrometer approach. In such methods, an initial estimateof the emittance can be used to improve the accuracy of themeasurements. One important aspect here concerns the effect of straylight on the accuracy of measurements. Such light can be reflected fromthe wafer and then be detected by the pyrometer, introducing error inthe temperature measurement. By having accurate estimates of the waferreflectance, the amount of reflected stray light can be estimated moreaccurately and hence its effect can be taken into account in determiningthe wafer temperature. Furthermore, in cases where the wafer issemi-transparent, it is usually necessary to know both the transmittanceand the reflectance of the wafer in order to determine the emittance ofthe wafer, for example from equations 8 or 13. The method of the currentinvention can also be used to determine transmittance and emittance asneeded. The measurement of transmittance can also help to obtainestimates of the amount of stray radiation transmitted by the substrate,which can be taken into account when interpreting the sensed radiationin order to determine the temperature of the wafer.

In some cases, measurements of transmittance and/or reflectance can alsobe used to determine the wafer temperature. For example, if we know thetemperature dependence of either of these quantities at a givenwavelength then we can use an in situ measurement of either of them todetermine the wafer temperature. The advantage of this approach is thatit is no longer necessary to measure the radiation emitted by the wafer.Such an approach can also be made insensitive to stray light problems.It can also be applied at relatively low temperatures, where pyrometrycan be very difficult because of the low intensity of thermally emittedradiation. The temperature dependence of reflectance or transmittancecan be estimated using the methods described in this invention, even incases where there is not a prior knowledge of the coating that may bepresent on either surface of the wafer. For example, the reflectivitiesof the front and back surface of the wafer can be obtained as described.The temperature dependence of the absorption coefficient of silicon canbe obtained from a model as described earlier, and this can be combinedwith the measured reflectivities to provide estimates of the temperaturedependence of the transmittance or reflectance as needed. Hence in thisexample, the parameter that is modeled is the temperature dependence ofthe transmittance or the reflectance.

The parameter may also be one that is used in a control algorithm thatdetermines a setting for a characteristic of the heating system. Thatcharacteristic influences the energy delivered to the wafer or theenergy that is lost from the wafer, and hence affects the temperature,the heating rate or the cooling rate of the wafer. These quantities maybe affected across the whole of the wafer or they may be affected in aparticular region of the wafer. In the latter case, the wafertemperature uniformity can be affected by alteration of the systemcharacteristic. The characteristic of the system may be a processvariable, such as the power or energy delivered by a heating lamp orenergy beam, the temperature and position of a heat radiating element,the current or voltage applied to an electrical conductor, the magnitudeof RF or microwave power, or the magnitude of a gas flow. Other examplesof process variables include the composition of gases in the chamber andtheir pressure, direction of flow etc. The characteristic can also be aphysical characteristic of the heating system, such as the position of areflector, the reflectance of a reflector, the location and size of aheating beam of energy, the wavelength, angle of incidence or state ofpolarization of an beam of electromagnetic energy, the location of aheat source relative to the wafer position, the magnitude of the gapbetween a wafer and a hot-plate or between the wafer and a heat-sinketc.

The parameter supplied to the control algorithm can be any factor thatinfluences the thermal response of the wafer. The control algorithm canbe a model-based controller. For example the algorithm can predictdesirable settings for process or system variables in order to keep thewafer temperature on a given heating cycle, and/or to maintain a desireddegree of temperature uniformity within the wafer. The predictions canbe based on a model of heat transfer phenomena occurring during theprocessing. Clearly, by providing better information about waferproperties to the model, it is possible to improve the fidelity of themodel to reality and hence to obtain better estimates of the process orsystem variables. The control algorithm may operate in an open-loopmode, where the settings are predicted on the basis of the model. It mayalso operate in a closed-loop mode, where the algorithm is provided withfeedback about the wafer condition from at least on sensor. In thelatter case, the control algorithm may also use a model of the heattransfer phenomena to improve the selection of control settings. Indeedthe algorithm can include a part that predicts approximate values forthe control settings based on predictions from the model, and a secondpart that corrects those settings to take account of the informationfrom the sensor.

As mentioned earlier, the parameter supplied to the controller can be aphysical characteristic, such as the wafer thickness. In case where thewafers are heated by optical or thermal radiation or where the waferloses heat by radiation, the optical properties of the wafer may alsoaffect the thermal response. Hence the parameter may be an emittance, anabsorptance, a reflectance or a transmittance. In general it can relateto any property that describes how a wafer emits, absorbs, reflects,transmits or scatters electromagnetic radiation. Earlier, the use of themethods of this disclosure were discussed to identify whether a wafer isheavily doped or lightly doped. Such information can be provided to thecontrol algorithm, or can even be used to select an appropriate controlalgorithm that takes into account how heavily doped material is expectedto couple to an energy source. A selection of a control algorithm canaffect the heating recipe structure if desired. Likewise, if it isdetermined that the wafer has a metal coating on a surface, the controlalgorithm can take this factor into account. The algorithm can determinehow energy is applied to the wafer, including what intensity to apply towhich location on the wafer and for what duration. It can also determinewhether to operate in an open-loop mode of heating or in a closed-loopmode of heating, where feedback from at least one sensor of wafercondition is used to control the process. In some cases, there may be atransition between closed-loop and open-loop modes of operation that isdetermined by a criterion selected on the basis of the premeasurementsof wafer properties. For example, it may be determined that if the waferis predicted to be sufficiently opaque at a given temperature then thereadings from a temperature sensor are valid when the sensor reportsthat the wafer is at a temperature above a given temperature. In thiscase, the controller can select a closed-loop control approach once thisgiven temperature is reached during the initial heat up step.

The next step is processing of the wafer. The parameter is used by thecontrol or measurement algorithm to provide more accurate or repeatableor uniform treatment, or to provide a faster or more efficient way ofprocessing. Typical processes can include thermal annealing,crystallization, alloying, sintering, oxidation, nitridation, filmdeposition, etching, and promotion of reactions between materialsdeposited on a wafer, or between materials on a wafer and a process gas.

The final step involves unloading the wafer.

FIG. 22 shows another flow diagram for the present disclosure. In thiscase the diagram explicitly includes the possibility of measuring theoptical properties at multiple wavelengths and multiple wafertemperatures. The information from such a set of measurements can beused in the prediction of optical properties of the wafer at aprocessing temperature.

FIG. 23 shows another flow diagram explicitly showing a step where anoptical property of the wafer is determined using an approach where aparticular component from the reflected or transmitted rays is selectedfor the measurement. This might be a group of rays such as the raycalled R1 in FIG. 19, where the light has only been reflected from thefirst surface of the wafer. In that case the optical property that isdetermined could be the reflectivity of the front surface (WF), R_(tv.)

FIG. 24 shows an example, where the approach of measuring thereflectivity of a surface is used to predict an emittance at theprocessing temperature. The emittance value can be predicted with a verysimple model, such as ε_(WF)=1−R_(tv). The emittance can be used tocorrect readings from a pyrometer. It can also be used to estimate powercoupling to a heating energy source. It can also be used to estimateheat loss from the wafer surface. The determination of reflectivity andemittance can be made at a single wavelength, or it can be made over arange of wavelengths.

FIG. 25 shows another flow diagram illustrating an example where thepre-measurements are used to determine a doping characteristic of awafer. The doping characteristic is then taken into account when makinga prediction of an optical property at the process temperature. Thisoptical property is then used to determine a parameter that is used formonitoring or controlling the process. The parameter can be a thresholdtemperature criterion for determining whether the temperature readingfrom a pyrometer is valid. It can also be a wafer emittance orabsorptance. The parameter can also be a flag that tells the controlsystem what kind of temperature measurement or control algorithm to use.It can also be used to determine what kind of temperature sensor to use.For example, if the wafer is determined to be heavily-doped (e.g. with aresistivity <0.1 Ωcm), then the system can chose to measure the wafertemperature with a pyrometer, for temperatures in a given range. On theother hand if the wafer is determined to be lightly doped (e.g. with aresistivity >0.1 Ωcm) the temperature can be measured by a sensor basedon the transmission of infra-red light through the substrate. Thedetermination of a doping characteristic can also be used to improve theaccuracy of temperature measurement. For example, if an infra-redtransmission measurement is used to determine wafer temperature, thenknowledge about the doping characteristic of the wafer can be used tocorrect for the influence of wafer doping on infra-red transmission, anda more accurate estimate of the wafer temperature can be obtained.

FIG. 26 shows another flow diagram, illustrating an example whereinformation about wafer thickness is used to provide a parameter that isprovided to the measurement or control system. The parameter can be thethickness itself. For example, a model-based controller may use thethickness information to predict the heating or cooling rate of thewafer. It may also use the thickness information to predict the timetaken by the wafer to reach a given temperature. This approach can beused to improve the repeatability of heating processes. The waferthickness can be provided as an input to the processing system or it canbe measured by hardware in the processing system. The thicknessinformation might also be used to predict optical properties of thewafer.

Any of the flow-diagram approaches or methods described in thisdisclosure can be combined as necessary.

These and other modifications and variations to the present inventionmay be practiced by those of ordinary skill in the art, withoutdeparting from the spirit and scope of the present invention. Inaddition, it should be understood that aspects of the variousembodiments may be interchanged both in whole or in part. Furthermore,those of ordinary skill in the art will appreciate that the foregoingdescription is by way of example only, and is not intended to limit theinvention.

1. A method for controlling a heating process for substrates comprising:emitting light onto a first surface of a substrate, the substrateincluding the first surface and a second and opposite surface separatedfrom the first surface by a thickness; directing the light through anoptical pathway that separates the light reflected from the firstsurface from light reflected from the second surface; detecting theamount of light reflected from the first surface; and based on theamount of detected light reflected from the first surface, controllingor adjusting at least one system component in a process for heating thesubstrate.
 2. A method as defined in claim 1, wherein the systemcomponent comprises a temperature measurement system that includes aradiation measuring device that senses the amount of radiation beingemitted by the substrate during heating for determining a temperature ofthe substrate, the amount of detected light from the first surface beingused to determine an emittance for the substrate for use in determiningthe temperature of the substrate in conjunction with the amount ofradiation being sensed by the radiation measuring device.
 3. A method asdefined in claim 1, wherein the system component comprises a heatingsystem including a power controller for a heating device that is used toheat the substrate, the amount of detected light from the first surfacebeing used to determine absorptance of the substrate for adjusting thepower controller and thereby selectively increasing or decreasing theamount of energy being used to heat the substrate.
 4. A method asdefined in claim 1, further comprising the step of: detecting the amountof light reflected from the second surface of the substrate; and whereinthe system component comprises a temperature measurement system thatincludes a radiation measuring device that senses the amount ofradiation being emitted by the substrate during heating for determininga temperature of the substrate, the amount of detected light from thefirst surface and the amount of detected light from the second surfacebeing used to determine emittance, transmittance, reflectance, orcombinations thereof for the substrate for use in determining thetemperature of the substrate in conjunction with the amount of radiationbeing sensed by the radiation measuring device.
 5. A method as definedin claim 1, wherein the substrate is heated in a thermal processingchamber and the light is emitted onto the first surface of the substrateoutside of the thermal processing chamber and, after the amount of lightreflected from the first surface is detected, the substrate istransferred into the thermal processing chamber.
 6. A method as definedin claim 1, wherein the light is emitted onto the first surface of thesubstrate at a temperature below 100° C.
 7. A method as defined in claim1, wherein the substrate is heated by light energy sources, by a heatedsusceptor, by radio frequency, by microwave energy, by a hot wallenvironment, by convective heating, by conductive heating, by heatingwith energy beams, such as plasma beams, electron beams, or ion beams,or by a mixture thereof during the heating process.
 8. A method asdefined in claim 2, wherein the radiation measuring device sensesradiation being emitted by the substrate at a certain wavelength andwherein the amount of light that is reflected from the first surface ofthe substrate is detected at the same wavelength at which the radiationmeasuring device operates, the light being emitted onto the firstsurface of the substrate at a temperature below about 100° C.
 9. Amethod as defined in claim 8, wherein the amount of detected light fromthe first surface of the substrate is used to determine reflectance oremittance of the substrate at temperatures where the transmittance ofthe substrate is less than 0.1 at the wavelength at which the radiationsensing device operates.
 10. A method as defined in claim 3, whereinduring the heating process, the substrate is heated by electromagneticradiation at a range of wavelengths and wherein the light that isreflected from the first surface of the substrate and detected is at awavelength range that substantially overlaps the range of wavelengths ofthe electromagnetic radiation that heats the substrate.
 11. A method asdefined in claim 5, wherein the system component comprises a temperaturemeasurement system that includes a radiation measuring device thatsenses the amount of radiation being emitted by the substrate duringheating for determining a temperature of the substrate, the amount ofdetected light from the first surface being used to determine anemittance for the substrate for use in determining the temperature ofthe substrate in conjunction with the amount of radiation being sensedby the radiation measuring device and wherein the radiation measuringdevice senses radiation being emitted by the substrate at a certainwavelength and wherein the amount of light that is reflected from thefirst surface of the substrate is detected at the same wavelength atwhich the radiation sensing device operates, the light being emittedonto the first surface of the substrate at a temperature below about100° C.
 12. A method as defined in claim 11, wherein the amount ofreflected light that is detected from the first surface of the substrateand the amount of reflected light that is detected from the secondsurface of the substrate are used to determine a reflectivity of bothsurfaces of the substrate, the reflectivities being used to determinetransmittance or emittance of the substrate at temperatures where thetransmittance of the substrate is greater than 0.1 at the wavelength atwhich the radiation measuring device operates.
 13. A method as definedin claim 10, further comprising the step of detecting the amount oflight that is reflected from the second surface of the substrate, theamount of reflected light detected from the first surface of thesubstrate and the amount of reflected light detected from the secondsurface of the substrate being used to determine the reflectivity ofeach surface, the reflectivity of each surface being used to determinethe absorptance of the substrate at temperatures where the transmittanceof the substrate is less than 0.1 at the wavelength range of theelectromagnetic radiation that is used to heat the substrate.
 14. Amethod as defined in claim 1, wherein the optical pathway includes atleast two optical devices.
 15. A method as defined in claim 14, whereinthe at least two optical devices comprise a first lens and a secondlens.
 16. A method as defined in claim 14, wherein the optical pathwayincludes a first optical device and a second optical device which directthe light onto a particular location of the first surface of thesubstrate, the light reflecting off the first surface then once againpassing through the second optical device, from the second opticaldevice, the light is reflected off a third optical device and contacts afourth optical device so as to be focused onto a light detector.
 17. Amethod as defined in claim 15, wherein the light reflected from thefirst surface is separated from the light reflected from the secondsurface by at least in part adjusting a focal length of the first lensand a focal length of the second lens.
 18. A method as defined in claim14, wherein the light reflected from the first surface is separated fromthe light reflected from the second surface at least in part by using ablocking device.
 19. A method as defined in claim 1, wherein the lightthat is emitted onto the first surface of the substrate comprises alaser beam.
 20. A method as defined in claim 14, wherein the at leasttwo optical devices comprise lenses, mirrors, or mixtures thereof.
 21. Amethod as defined in claim 1, wherein the light that is emitted onto thefirst surface of the substrate is generated by a broad band lightsource.
 22. A method for determining at least one optical characteristicof a substrate comprising: emitting light onto a first surface of asubstrate, the substrate including the first surface and a second andopposite surface separated from the first surface by a thickness;directing the light through an optical pathway that separates the lightreflected from the first surface from light reflected from the secondsurface; detecting the amount of light reflected from the first surface;and based on the amount of detected light reflected from the firstsurface, determining at least one optical characteristic of thesubstrate, the characteristic comprising a reflectivity, an emissivity,absorptivity, or a transmissivity of the first surface, or areflectance, an emittance, an absorptance, or a transmittance of thesubstrate, or mixtures of any of the above.
 23. A method as defined inclaim 22, wherein the optical characteristic of the substrate isdetermined at a specific light wavelength range.
 24. A method as definedin claim 23, wherein the specific light wavelength range comprises awavelength at which a radiation sensing device operates that is used tomeasure a temperature of the substrate.
 25. A method as defined in claim23, wherein the light wavelength range substantially overlaps with awavelength range of electromagnetic radiation that is used to heat thesubstrate.
 26. A method as defined in claim 22, wherein after the atleast one optical characteristic of the substrate is determined, thesubstrate is placed in a thermal processing chamber and heated, andwherein at least one system component is controlled during the heatingprocess based on the at least one optical characteristic.
 27. A methodas defined in claim 22, wherein the at least one optical characteristicof the substrate is determined in a thermal processing chamber thatheats the substrate.
 28. A method as defined in claim 22, wherein thesubstrate comprises a semiconductor wafer and wherein at least onesystem component of a semiconductor wafer processing system iscontrolled based upon the at least one optical characteristic.
 29. Amethod as defined in claim 26, wherein the system component comprises atemperature measurement system that includes a radiation measuringdevice that senses the amount of radiation being emitted by thesubstrate during heating for determining a temperature of the substrate,the amount of detected light from the first surface being used todetermine an emittance value for the substrate for use in determiningthe temperature of the substrate in conjunction with the amount ofradiation being sensed by the radiation measuring device.
 30. A methodas defined in claim 26, wherein the system component comprises a heatingsystem including a power controller for a heating device that is used toheat the substrate, the amount of detected light from the first surfacebeing used to adjust the power controller and thereby selectivelyincreasing or decreasing the amount of energy being used to heat thesubstrate.
 31. A method as defined in claim 26, further comprising thestep of: detecting the amount of light reflected from the second surfaceof the substrate; and wherein the system component comprises atemperature measurement system that includes a radiation measuringdevice that senses the amount of radiation being emitted by thesubstrate during heating for determining a temperature of the substrate,the amount of detected light from the first surface and the amount ofdetected light from the second surface being used to determineemittance, transmittance, reflectance, or combinations thereof for thesubstrate for use in determining the temperature of the substrate inconjunction with the amount of radiation being sensed by the radiationmeasuring device.
 32. A method as defined in claim 22, wherein theoptical pathway includes at least two optical devices.
 33. A method asdefined in claim 30, wherein the at least two optical devices comprise afirst lens and a second lens.
 34. A method as defined in claim 30,wherein the optical pathway includes a first optical device and a secondoptical device which direct the light onto a particular location of thefirst surface of the substrate, the light reflecting off the firstsurface then once again passing through the second optical device, fromthe second optical device, the light is reflected off a third opticaldevice and contacts a fourth optical device so as to be focused onto alight detector.
 35. A method as defined in claim 33, wherein the lightreflected from the first surface is separated from the light reflectedfrom the second surface by at least in part adjusting a focal length ofthe first lens and a focal length of the second lens.
 36. A method asdefined in claim 32, wherein the light reflected from the first surfaceis separated from the light reflected from the second surface at leastin part by using one blocking device.
 37. A method as defined in claim32, wherein the at least two optical devices comprise lenses, mirrors,or mixtures thereof.
 38. A method as defined in claim 34, wherein the atleast two optical devices comprise lenses, mirrors, or mixtures thereof.